Jie Wu
Research Fund:
National Science Foundation of the US, principal investigator, Project title: homotopy theory and its applications, 19992002.
(Note. The project was cancelled after it was approved, as I was coming to NUS in 1999.)
National University of Singapore Academic
Research Fund:
Principal Investigator, Project title:
Homotopy and Homology of Simplicial and Combinatorial Groups, 19992002;
Principal Investigator, Project title:
Representations in Homotopy Theory and Low Dimensional Topology, 20032006.
ACADEMIC RESEARCH FUND (AcRF), MOE, Singapore, TIER 1: Principal Investigator, Project title:
Homotopy of Braid Groups and Loop Spaces , 16/05/200715/05/2010.
ACADEMIC RESEARCH FUND (AcRF), MOE, Singapore, TIER 1: Principal Investigator, Joint with Jon Berrick, Project title:
Structures of braid and mapping class groups , 01/09/201031/08/2012.
ACADEMIC RESEARCH FUND (AcRF), MOE, Singapore, TIER 2: Principal Investigator, Joint with Jon Berrick, Project title:
Mapping class groups: topology and Ktheory aspects , 01/08/201131/07/2014.
Overseas Chinese Collaboration Fund of NSFC of China, preceding support: Principal Investigator, Project title:
homotopy theory and low dimensional topology, 01/01/201131/12/2012.
Overseas Chinese Collaboration Fund of NSFC of China: Principal Investigator, Project title:
homotopy theory and low dimensional topology, 01/01/201431/12/2017.
ACADEMIC RESEARCH FUND (AcRF), MOE, Singapore, TIER 1: Principal Investigator, Project title:
combinatorial and toric homotopy , 01/02/201431/01/2016.
PUBLICATIONS:

On the homology of stable function spaces, Acta Math.
Sinica, 34 (5) (1991), 703709.

F. Cohen and Jie Wu, A remark on the homotopy groups of
Σ^{n}RP^{2}, Contemporary Mathematics,
181(1995), 6581.
 On combinatorial descriptions of the
homotopy groups of
certain spaces, Math. Proc. Camb. Phil. Soc. 130 (2001),
no.3, 489513.

On fibrewise simplicial monoids and the
MilnorCarlsson
construction, Topology, 37(1998), No. 5, 11131134.

On combinatorial calculations of the
JamesHopf
maps, Topology, 37(1998), No. 5, 10111023.

A product decomposition of
Ω^{3}_{0}(ΣRP^{2}), Topology, 37(1998), No. 5, 10251032.

On products on minimal
simplicial sets
, J. of Pure and Appl. Algebra, 148 (2000), No. 1, 89111.

On the homology of configuration
spaces C((M,M_{0})×R^{n};X),
Math. Z., 22(1998), 235248.

Paul Selick and Jie Wu, On natural
coalgebra decompositions of tensor algebras and loop suspensions
, Memoirs AMS, Vol. 148, No. 701, 2000.
 Sections 14
 Sections 57
 Section 8
 Sections 910
 Section 11 (Examples)

Jie Wu, Murray Gerstenhaber and Jim Stasheff, On the Hodge decomposition of differential graded
bialgebras, J. of Pure and Appl. Algebra,
162(2001), No. 1, 10325.

Paul Selick and Jie Wu, On functorial
decompositions of selfsmash products,
Manuscripta Math. 111 (2003), no. 4, 435457. .

Paul Selick and Jie Wu, The functor
A^{min} on plocal spaces, Math. Zeit, 253 (2006), no. 3, 435451. .

A braided simplicial group
Proc. London Math. Soc., (3) 84 (2002), no. 3, 645662.

On co$H$maps to the suspension of the
projective plane, Topology and its Applications,
123(2002), 547571.

Paul Selick and Jie Wu, Some Calculations
of Lie^{max}(n) for low n, J. of Pure and Appl. Algebra,
(11)212 2008, 25702580.

Fred Cohen and Jie Wu,
Artin's braid groups, free groups, and the loop space of
the $2$sphere,
Quarterly J. Math., 62 (2011), no. 4, 891¨C921.
 Fred Cohen and Jie Wu, On braids,
free groups and the loop space
of the 2sphere,
Progress in Mathematic Techniques, Vol.215 (2004):
Algebraic Topology: Categorical Decompositions, 93105.

A. J. Berrick, F. R. Cohen, Y. L. Wong and J. Wu, braids, configurations and homotopy
groups, J. Amer. Math. Soc. 19 (2006), no. 2, 265326.

Homotopy theory of the suspensions of
the projective plane, Memoirs AMS, Vol. 162, No. 769, 2003.

Paul Selick, Stephen Theriault and Jie Wu, Functorial
decompositions of looped coassociative coH spaces, Canadian J. Math., 58 (2006), no. 4, pp.877896.
 On maps from loop suspensions to loop spaces and the
shuffle relations on the Cohen groups. Memoirs AMS, Vol. 180, No. 851, 2006.
 Jelena Grbic and Jie Wu, Natural transformations of tensor algebras
and representations of combinatorial groups.
Algebraic & Geometric Topology 6 (2006) 21892228.
 Jelena Grbic and Jie Wu, Applications of combinatorial groups to the Hopf invariants and the
exponent problem. Algebraic & Geometric Topology 6 (2006) 22292255.
 F. R. Cohen and J. Wu, On braid groups and homotopy groups, Geometry & Topology
Monographs 13 (2008) 169193
 F. R. Cohen, J. Pakianathan, V. Vershinin, and J. Wu,
Basisconjugationg automorphisms of a free group and asscociated Lie algebras, Geometry & Topology Monographs 13 (2008) 147168
 EHP sequences for (p1)cell complexes and the functor A^{min}, Israel J. Math., 178 (2010), 349391.
 Jingyan Li and Jie Wu, Artin Braid Groups and Homotopy Groups, Proc. London Math. Soc., 99 No. 3 (2009), 521556.
 Fengchun Lei and Jie Wu, The intersecting kernel of Heegaard Splittings, Algebraic & Geometric Topology, 11 (2011), 887908.
 Jelena Grbic, Paul Selick and Jie Wu, The decomposition of the loop space of the mod 2 Moore space,
Algebraic & Geometric Topology 8 (2008) 945951.
 Paul Selick, Stephen Theriault and Jie Wu, functorial homotopy decompositions of looped coHspaces,
Math Z., 267 (2011), Numbers 12, 139153.
 J. Grbic, S. Theriault and J. Wu, suspension splittings and
Hopf invariants for retracts of the loops on coHspaces, Proc. Roy. Soc. Edinburgh Sect. A 144 (2014), no. 1, 87?08.
 J. Li, F. Lei and J. Wu, Module structure on Lie powers and
natural coalgebrasplit sub Hopf algebras of tensor algebras, Proc. Edinburgh Math Soc., 54 (2011), 467504.
 Jingyan Li and Jie Wu, On symmetric commutator
subgroups, braids, links and homotopy groups, Trans. Amer. Math. Soc, 363 (2011), 38293852.
 V. G. Bardakov, R. V. Mikhailov, V. V. Vershinin and J. Wu,
On the pure virtual braid group PV_{3,}
Comm. Algebra 44 (2016), no. 3, 13501378.
 V. G. Bardakov, R. V. Mikhailov, V. V. Vershinin and J. Wu,
Brunnian braids on surfaces
Algebraic & Geometric Topology, 12(2012), 16071648.
 R. V. Mikhailov and J. Wu, On homotopy groups of the suspended classfying spaces,
Algebraic & Geometric Topology, 10 (2010) 565625.
 A. J. Berrick, F. Duzhin and J. Wu, braid groups, free groups and permutative actions, preprint.
 A. J. Berrick, E. Hanbury and J. Wu,
Deltastructures on mapping class groups and braid groups, Trans. Amer. Math. Soc. 366 (2014), no. 4, 18791903.
 A. J. Berrick, E. Hanbury and J. Wu,
Brunnian subgroups of mapping class groups and braid groups, Proc. Lond. Math. Soc. (3) 107 (2013), no. 4, 875906.
 Fuquan Fang, Fengchun Lei, and Jie Wu, The symmetric commutator homology of link towers and homotopy groups of 3manifolds,
Commun. Math. Stat. 3 (2015), no. 4, 497526.
 R. V. Mikhailov, I. B. S. Passi and J. Wu, On symmetric products of ideals in group rings and simplicial homotopy, JPAA,
215 (2011), 10851092.
 P. Beben and J. Wu, Modular representations and the homotopy of low rank plocal CWcomplexes, Math. Z.,
23 (2013) 735751.
 P. Beben and J. Wu, The homotopy type of a Poincare duality complex after looping,
Proc. Edinburgh Math Soc. (2) 58 (2015), 581616.
 Junda Chen, Zhi Lu and Jie Wu,
Orbit configuration spaces of small covers and quasitoric manifolds, preprint.
 Fengchun Lei, Fengling Li and Jie Wu,
On simplicial resolutions of framed links,
Trans. Amer. Math. Soc. 366 (2014), no. 6, 30753093.
 J. Grbic, S. Theriault and J. Wu,
Decompositions of looped co$H$spaces, Proc. AMS, 141 (2013) 14511464.
 J. Grbic and J. Wu, On the homotopy rigidity of the functor $\Sigma\Omega$ on coHspaces, Adv. Math. 273 (2015), 523539.
 Jelena Grbic, John Harper, Mamoru Mimura, Stephen Theriault and Jie Wu,
Rank p1 modp Hspaces, Israel J. Math., 194 (2013), 641688.
 R. V. Mikhailov and J. Wu,
Combinatorial group theory and the homotopy groups of finite complexes, Geometry & Topology, 17 (2013), 235272.
 R. V. Mikhailov and J. Wu,
Homotopy groups as centers of finitely presented groups,
Izv. Math., 77 (2013), 581593.
 Jie Wu, Groups with structures and homotopy groups, Handbook of group actions. Vol. II, 371396,
Adv. Lect. Math. (ALM), 32, Int. Press, Somerville, MA, 2015.
 Bardakov, V.; Gongopadhyay, K.; Singh, M.; Vesnin, A.; Wu, J. Some problems on knots, braids, and automorphism groups.
Sib. ¨¨lektron. Mat. Izv. 12 (2015), 394405.
 Jelena Grbic, Taras Panov, Stephan Theriault and Jie Wu, Homotopy types of momentangle complexes
, Trans. Amer. Math. Soc. 368 (2016), no. 9, 66636682.
 Weidong Chen and Jie Wu,
Decomposition of loop spaces and periodic problem on $\pi_*$, Algebraic & Geometric Topology 13 (2013) 32453260.
 Man Gao and Jie Wu, Homology decompositions of the loops on 1stunted Borel
constructions of C_{2}actions Algebraic & Geometric Topology 13 (2013) 31753201.
 Man Gao and Jie Wu, Simplicial Monoid Actions and The Associated Universal Simplicial Monoid Construction,
J. Homotopy Relat. Struct. 11 (2016), no. 2, 199208.
 Gao, Man; Tan, Colin; Wu, Jie Loop homological invariants associated to real projective spaces. Topology Appl. 209 (2016), 275288.
 V. G. Bardakov, V. V. Vershinin and J. Wu, On Cohen braids, Proc. Steklov Inst. Math. 286 (2014), 1632.
 J. Y. Li, V. V. Vershinin and J. Wu, Brunnian braids and Lie algebras, J. Algebra 439 (2015), 270293.
 J. Y. Li, V. V. Vershinin and J. Wu,
Twisted simplicial groups and twisted homology of categories, Homology Homotopy Appl. 19 (2017), no. 2, 111130.
 Lei, Fengchun; Wu, Jie; Zhang, Yu On intersecting subgroups of Brunnian link groups. Algebr. Geom. Topol.
16 (2016), no. 2, 10431061.
 Li, Fengling; Lei, Fengchun; Wu, Jie 3manifold invariants derived from the intersecting kernels. Internat. J. Math.
27 (2016), no. 13, 1650109, 9 pp.
 Sergei O. Ivanov, Roman Mikhailov and Jie Wu,
On nontriviality of homotopy groups of spheres,Homology Homotopy Appl. 18 (2016), no. 2, 337344.
 Roman Mikhailov and Jie Wu,
On the metastable homotopy of mod 2 Moore spaces, Algebr. Geom. Topol. 16 (2016), no. 3, 17731797.
 Wu, Jie; Yuan, Zihong Stable functorial decompositions of $F(\mathbb{R}^{n+1},j)^{+}\wedge_{\Sigma_j}X^{(j)}$,
Algebr. Geom. Topol. 17 (2017), no. 2, 895915.
 Musin, Oleg R.; Wu, Jie Cobordism classes of maps and covers for spheres. Topology Appl. 237 (2018), 2125.
 Li, Zhiguo; Lei, Fengchun; Chen, Zhi; Wu, Jie On fundamental group of a certain class of welded knots.
Commun. Math. Res. 33 (2017), no. 2, 177184.
 Sergei O. Ivanov, Roman Mikhailov and Jie Wu,
Homotopy theory and generalized dimension subgroups, J. Algebra 484 (2017), 224246.
 Liang, Liang; Li, Fengling; Lei, Fengchun; Wu, Jie Local uniqueness of certain geodesics related to Heegaard splittings.
J. Knot Theory Ramifications 27 (2018), no. 9, 1842003, 9 pp.
 Huang, Ruizhi; Wu, Jie On mod p A_{p}spaces. Algebr. Geom. Topol. 17 (2017), no. 4, 21252144.
 Sergei O. Ivanov, Roman Mikhailov and Jie Wu,
Leibniz rule on higher pages of unstable spectral sequences, Proc. Edinb. Math. Soc. (2) 61 (2018), no. 1, 265282.
 Frederick R. Cohen, Roman Mikhailov and Jie Wu,
A combinatorial approach to the exponents of Moore spaces, Math. Z. 290 (2018), no. 12, 289305.
.
Selected Talks

On combinatorial descriptions of homotopy
groups
This topic has been talked in: Unstable Homotopy Theory Session the
academic year on homotopy theory at
The Fields Institute (199596); The Ontario Topology Seminar (1996);
AMSIMSSIAM Joint Summer Research Conference at Mount Holyoke College
(1994); MSRI, Berkeley (199596); AMS Meeting at Kent State University
(1994); AMS Meeting at University of California at San Diego (1997);
University of Rochester (1994); Northwestern University (1995); Department
Colloquium of the Lehigh University (1998); Department Colloquium of the
National University of Singapore (1998).
New progress on this topic: Talked at the
National University of Singapore (2000). Further relations between the
homotopy and the links will be talked at the University of
Rochester (2000).

Functorial decompositions of
loop spaces of suspensions, and their relation to representation
theory
This topic has been talked at the University of Pennsylvania (1997); MIT
(1997); University of Rochester (1998); National University of Singapore
(1998).

Representations and Homotopy
Theory; another talk on this topic
This topic has been talked twice at the National University of Singapore
(19992000).

Exponent Problems in Homotopy Theory
Talked at the National University of Singapore (19992000).

Configurations in homotopy theory
Talked at the National University of Singapore (19992000).

Homotopy groups and braids
Talked at the University of Rochester (October, 2000).

Homotopy groups and braids, talked at
Okayama University of Science, Okayama, Japan, on May 24, 2001.

Representations in homotopy theory,
talked at the Shinshu University, Matsumoto, Japan, on May 26,
2001.

On the Homotopy Groups of the sphere and the braid groups,
talked at International Conference in Algebraic Topology
Isle of Skye  Scotland 2430 June 2001.
 Braids, Mapping Class Groups and the Homotopy Groups talked at
the SingaporeWarwick Workshop on Geometry and Topology, July 2001.
 The $LS$category of Certain $3$cell Complexes talked at AMSIMSSIAM Summer Research
Conference on LusternikSchnirelmann Category, July 29August 02, 2001.
 braids and homotopy groups,talked
at Beijing University, June, 2002.
 homotopy decompositions of
spaces, talked at Beijing University, June, 2002.
 representation theory in homotopy,
talked at ICM satellite conference on algebraic topology, Suzhou,
China, August 30September 3, 2002.
 Braids, configurations and homotopy groups,
talked at Mathematics Institute in Oberwolfach, Germany, March 18,
9:3010:30, 2003.
 Representation Theory in Homotopy,
talked at Ecole Polytechnique Federale de
Lausanne, December 9, 2003.
 Braids and Homotopy Groups,
talked at Universite Montpellier II, December 18, 2003.
 The Exponent Problem in Homotopy Theory,
talked at University of Paris 13, December 19, 2003.
 Braids and Homotopy Groups,
talked at International conference on Homotopy theory and related
topics, February 25, 2004, Korea; 33:45 pm Feb. 3.
 The Exponent Problem in Homotopy Theory,
talked at International conference on Homotopy theory and related
topics, February 25, 2004, Korea; 33:45 pm Feb. 4.
 Braids and Homotopy Groups,
talked at Nankai University, 46 pm June 8, 2004.
 Homotopy Groups, Configuration Spaces and the Braid Groups,
talked at Zhejiang University, 910 am July 5, 2004.
 The Exponent Problem and Cohen Groups talked at Department of Mathematics, University of Rochester, 45 pm,
January 26, 2005.
 Cohen Groups talked at "International conference on Homotopy theory and related
topics, February 14, 2005, Korea; Premeeting on January 31.
 Configuration Spaces and the Evaluation Maps talked at "International
conference on Homotopy theory and related
topics", February 14, 2005, Korea. 2:303:15 pm, February 1.
 The Exponent Problem and Cohen Groups talked at Department of Mathematics, MIT, March 28, 2005
 Shuffle relations on the Cohen groups talked at "Special Session on Homotopy Theory in Honor of
Don Davis' and Martin Bendersky's 60th Birthdays,
2005 AMS Spring Eastern Sectional Meeting", Newark, Delaware, April 23, 2005.
 Homotopy groups and Braids talked at Department of Mathematics, Columbia University, April 29,
2005.
 Representations in classical homotopy theory talked at "Annual Conference on Algebraic Topology",
Matsumoto, Japan, July 1316, 2005.
 From braid groups to homotopy Groups talked at the Third Pacific Rim Conference
on Mathematics, Fudan University, Shanghai, China, August 17?1,2005. (1:302:15pm August 17, 2005)
 The Exponent Problem and Cohen Groups talked at "`Stable and algebraic homotopy", Schloss Ringberg, Germany,
October 30November 5, 2005.
 Decompositions of loop spaces talked in International Conference on Algebraic Topology,
Kyoto, Japan, December 58, 2005.
 Homotopy Groups Talked at NUS Summer School, 9:3010:30, May 25, 2006.
 Hspaces with rectractile generating complexes talked in International
Conferences on Geometric Topology, Capital Normal University, China, June 1618, 2006.
 The functor A^{min} talked in Topology Conference in honor of the 90th birthday
of Professor Zhang SuCheng, Institute of Mathematics, Chinese Academy of Sciences,
July 1011, 2006.
 Braid Groups, 5hour lectures in the International Summer School
on Geometric Topology, Liaoning Normal University, Dalian, China, July 1928, 2006.
 EHPsequences for (p1)cell complexes International Conference in Algebraic
Topology, Henan University, Kai Feng, Henan, China, October 1518, 2006.
 Topology and Poincare Conjecture, Mathematics Enrichment Camp 2006, National University of Singapore,
11:3012:30
December 14, 2006
 Simplicial Objects and Homotopy Groups, 4hour lecture, Program on Braids,
Institute of Mathematical Siences, National University of Singapore, 14 May 13 July, 2007.
 Mirror Reflections on Braids and the Higher Homotopy Groups of the 2sphere,
talked on June 21, 2007, in Geometric Topology ConferenceBeijing 2007, June 1822, 2007.
 Adams Spectral Sequences and the YangBaxter Lie algebra, talked on July 18, 2007,
in Algebraic and Differential Topology Conference at Nankai University, Tianjin, China, July 1822, 2007.
 Connections between algebraic topology and the theory of braids, Public Talk
of National Science Award 2007 of Singapore, September 20, 2007.
 Boundary Brunnian braids, mirror reflection and the homotopy groups, talked in 1st East Asia Conference on Algebraic Topology,
Seoul National University, Seoul, Korea. November 26, 2007
 Artin braid groups and the homotopy groupsJoint with Jingyan Li talked in
International Conference on Topology and its Applications 2007, Kyoto University, December 37,
A Joint conference with "4th Japan Mexico Topology Conference".
 Simplicial Structure on Braids and Homotopy Groups, talked in Topology Seminar
of Kyushu University on December 10, 2007.
 Braid Groups and Homotopy Groups II, talked in Topology Seminar
of Dalian University of Technology on December 18, 2007.
 Simplicial Objects, 4hour talks in Small Algebraic Topology Conference at
Fudan University, December 2023, 2007.
 Braids, configurations and homotopy groups, talked in Topology Seminar of
Hebei Normal University, December 31, 2007.
 Braid Groups and Homotopy Groups III, talked in Topology Seminar
of Dalian University of Technology on January 8, 2008.