# Research Fund:

• National Science Foundation of the US, principal investigator, Project title: homotopy theory and its applications, 1999-2002.
(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, 1999-2002;
• Principal Investigator, Project title: Representations in Homotopy Theory and Low Dimensional Topology, 2003-2006.
• ACADEMIC RESEARCH FUND (AcRF), MOE, Singapore, TIER 1:
Principal Investigator, Project title: Homotopy of Braid Groups and Loop Spaces , 16/05/2007-15/05/2010.
• ACADEMIC RESEARCH FUND (AcRF), MOE, Singapore, TIER 1:
Principal Investigator, Joint with Jon Berrick, Project title: Structures of braid and mapping class groups , 01/09/2010-31/08/2012.
• ACADEMIC RESEARCH FUND (AcRF), MOE, Singapore, TIER 2:
Principal Investigator, Joint with Jon Berrick, Project title: Mapping class groups: topology and K-theory aspects , 01/08/2011-31/07/2014.

• # PUBLICATIONS:

1. On the homology of stable function spaces, Acta Math. Sinica, 34 (5) (1991), 703-709.
2. F. Cohen and Jie Wu, A remark on the homotopy groups of ΣnRP2, Contemporary Mathematics, 181(1995), 65-81.
3. On combinatorial descriptions of the homotopy groups of certain spaces, Math. Proc. Camb. Phil. Soc. 130 (2001), no.3, 489-513.
4. On fibrewise simplicial monoids and the Milnor-Carlsson construction, Topology, 37(1998), No. 5, 1113-1134.
5. On combinatorial calculations of the James-Hopf maps, Topology, 37(1998), No. 5, 1011-1023.
6. A product decomposition of Ω30(ΣRP2), Topology, 37(1998), No. 5, 1025-1032.
7. On products on minimal simplicial sets , J. of Pure and Appl. Algebra, 148 (2000), No. 1, 89-111.
8. On the homology of configuration spaces C((M,M0)×Rn;X), Math. Z., 22(1998), 235-248.
9. Paul Selick and Jie Wu, On natural coalgebra decompositions of tensor algebras and loop suspensions , Memoirs AMS, Vol. 148, No. 701, 2000.
Sections 1-4
Sections 5-7
Section 8
Sections 9-10
Section 11 (Examples)
10. Jie Wu, Murray Gerstenhaber and Jim Stasheff, On the Hodge decomposition of differential graded bi-algebras, J. of Pure and Appl. Algebra, 162(2001), No. 1, 103-25.
11. Paul Selick and Jie Wu, On functorial decompositions of self-smash products, Manuscripta Math. 111 (2003), no. 4, 435--457. .
12. Paul Selick and Jie Wu, The functor Amin on p-local spaces, Math. Zeit, 253 (2006), no. 3, 435--451. .
13. A braided simplicial group Proc. London Math. Soc., (3) 84 (2002), no. 3, 645--662.
14. On co-$H$-maps to the suspension of the projective plane, Topology and its Applications, 123(2002), 547-571.
15. Paul Selick and Jie Wu, Some Calculations of Liemax(n) for low n, J. of Pure and Appl. Algebra, (11)212 2008, 2570-2580.
16. 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.
17. Fred Cohen and Jie Wu, On braids, free groups and the loop space of the 2-sphere, Progress in Mathematic Techniques, Vol.215 (2004): Algebraic Topology: Categorical Decompositions, 93-105.
18. 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, 265--326.
19. Homotopy theory of the suspensions of the projective plane, Memoirs AMS, Vol. 162, No. 769, 2003.
20. Paul Selick, Stephen Theriault and Jie Wu, Functorial decompositions of looped coassociative co-H spaces, Canadian J. Math., 58 (2006), no. 4, pp.877-896.
21. On maps from loop suspensions to loop spaces and the shuffle relations on the Cohen groups. Memoirs AMS, Vol. 180, No. 851, 2006.
22. Jelena Grbic and Jie Wu, Natural transformations of tensor algebras and representations of combinatorial groups. Algebraic & Geometric Topology 6 (2006) 2189-2228.
23. Jelena Grbic and Jie Wu, Applications of combinatorial groups to the Hopf invariants and the exponent problem. Algebraic & Geometric Topology 6 (2006) 2229-2255.
24. F. R. Cohen and J. Wu, On braid groups and homotopy groups, Geometry & Topology Monographs 13 (2008) 169-193
25. F. R. Cohen, J. Pakianathan, V. Vershinin, and J. Wu, Basis-conjugationg automorphisms of a free group and asscociated Lie algebras, Geometry & Topology Monographs 13 (2008) 147-168
26. EHP sequences for (p-1)-cell complexes and the functor Amin, Israel J. Math., 178 (2010), 349--391.
27. Jingyan Li and Jie Wu, Artin Braid Groups and Homotopy Groups, Proc. London Math. Soc., 99 No. 3 (2009), 521--556.
28. Fengchun Lei and Jie Wu, The intersecting kernel of Heegaard Splittings, Algebraic & Geometric Topology, 11 (2011), 887--908.
29. Jelena Grbic, Paul Selick and Jie Wu, The decomposition of the loop space of the mod 2 Moore space, Algebraic & Geometric Topology 8 (2008) 945-951.
30. Paul Selick, Stephen Theriault and Jie Wu, functorial homotopy decompositions of looped co-H-spaces, Math Z., 267 (2011), Numbers 1-2, 139--153.
31. J. Grbic, S. Theriault and J. Wu, suspension splittings and Hopf invariants for retracts of the loops on co-H-spaces, preprint.
32. J. Li, F. Lei and J. Wu, Module structure on Lie powers and natural coalgebra-split sub Hopf algebras of tensor algebras, Proc. Edinburgh Math Soc., 54 (2011), 467--504.
33. Jingyan Li and Jie Wu, On symmetric commutator subgroups, braids, links and homotopy groups, Trans. Amer. Math. Soc, 363 (2011), 3829--3852.
34. V. G. Bardakov, R. V. Mikhailov, V. V. Vershinin and J. Wu, On the pure virtual braid group PV3, preprint.
35. V. G. Bardakov, R. V. Mikhailov, V. V. Vershinin and J. Wu, Brunnian braids on surfaces Algebraic & Geometric Topology, 12(2012), 1607--1648.
36. R. V. Mikhailov and J. Wu, On homotopy groups of the suspended classfying spaces, Algebraic & Geometric Topology, 10 (2010) 565--625.
37. A. J. Berrick, F. Duzhin and J. Wu, braid groups, free groups and permutative actions, preprint.
38. A. J. Berrick, E. Hanbury and J. Wu, Delta-structures on mapping class groups and braid groups, Trans. Amer. Math. Soc, to appear.
39. A. J. Berrick, E. Hanbury and J. Wu, Brunnian subgroups of mapping class groups and braid groups, Proc. London Math. Soc., to appear.
40. Fuquan Fang, Fengchun Lei, and Jie Wu, On Brunnian-type links and the link invariants given by homotopy groups of spheres, preprint.
41. R. V. Mikhailov, I. B. S. Passi and J. Wu, On symmetric products of ideals in group rings and simplicial homotopy,
42. JPAA, 215 (2011), 1085--1092.
The lecture notes of I. B. S. Passi's talk in ICM 2010.
43. P. Beben and J. Wu, Modular representations and the homotopy of low rank p-local CW-complexes, Math. Z., 23 (2013) 735–-751.
44. P. Beben and J. Wu, The homotopy type of a Poincare duality complex after looping, Proc. Edinburgh Math Soc. to appear
45. Junda Chen, Zhi Lu and Jie Wu, Orbit configuration spaces of small covers and quasi-toric manifolds, preprint.
46. Fengchun Lei, Fengling Li and Jie Wu, On simplicial resolutions of framed links, Trans. Amer. Math. Soc, to appear.
47. J. Grbic, S. Theriault and J. Wu, Decompositions of looped co-$H$-spaces, Proc. AMS, 141 (2013) 1451--1464.
48. J. Grbic and J. Wu, On the homotopy rigidity of the functor $\Sigma\Omega$ on co-H-spaces, preprint.
49. Jelena Grbic, John Harper, Mamoru Mimura, Stephen Theriault and Jie Wu, Rank p-1 mod-p H-spaces, Israel J. Math., 194 (2013), 641–-688.
50. R. V. Mikhailov and J. Wu, Combinatorial group theory and the homotopy groups of finite complexes, Geometry & Topology, 17 (2013), 235--272.
51. R. V. Mikhailov and J. Wu, Homotopy groups as centers of finitely presented groups, Izv. Math., 77 (2013), 581--593.
52. Jelena Grbic, Taras Panov, Stephan Theriault and Jie Wu, Homotopy types of moment-angle complexes , preprint.
53. Weidong Chen and Jie Wu, Decomposition of loop spaces and periodic problem on $\pi_*$, Algebraic & Geometric Topology 13 (2013) 3245-3260.
54. Man Gao and Jie Wu, Homology decompositions of the loops on 1-stunted Borel constructions of C_2-actions
55. Algebraic & Geometric Topology 13 (2013) 3175-3201.
56. Man Gao and Jie Wu, Simplicial Monoid Actions and The Associated Universal Simplicial Monoid Construction, preprint

# Selected Talks

1. 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 (1995-96); The Ontario Topology Seminar (1996); AMS-IMS-SIAM Joint Summer Research Conference at Mount Holyoke College (1994); MSRI, Berkeley (1995-96); 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).
2. Functorial decompositions of loop spaces of suspensions, and their relation to representation theory
3. This topic has been talked at the University of Pennsylvania (1997); MIT (1997); University of Rochester (1998); National University of Singapore (1998).
4. Representations and Homotopy Theory; another talk on this topic This topic has been talked twice at the National University of Singapore (1999-2000).
5. Exponent Problems in Homotopy Theory Talked at the National University of Singapore (1999-2000).
6. Configurations in homotopy theory Talked at the National University of Singapore (1999-2000).
7. Homotopy groups and braids Talked at the University of Rochester (October, 2000).
8. Homotopy groups and braids, talked at Okayama University of Science, Okayama, Japan, on May 24, 2001.
9. Representations in homotopy theory, talked at the Shinshu University, Matsumoto, Japan, on May 26, 2001.
10. On the Homotopy Groups of the sphere and the braid groups, talked at International Conference in Algebraic Topology Isle of Skye - Scotland 24-30 June 2001.
11. Braids, Mapping Class Groups and the Homotopy Groups talked at the Singapore-Warwick Workshop on Geometry and Topology, July 2001.
12. The $LS$-category of Certain $3$-cell Complexes talked at AMS-IMS-SIAM Summer Research Conference on Lusternik-Schnirelmann Category, July 29-August 02, 2001.
13. braids and homotopy groups,talked at Beijing University, June, 2002.
14. homotopy decompositions of spaces, talked at Beijing University, June, 2002.
15. representation theory in homotopy, talked at ICM satellite conference on algebraic topology, Suzhou, China, August 30-September 3, 2002.
16. Braids, configurations and homotopy groups, talked at Mathematics Institute in Oberwolfach, Germany, March 18, 9:30-10:30, 2003.
17. Representation Theory in Homotopy, talked at Ecole Polytechnique Federale de Lausanne, December 9, 2003.
18. Braids and Homotopy Groups, talked at Universite Montpellier II, December 18, 2003.
19. The Exponent Problem in Homotopy Theory, talked at University of Paris 13, December 19, 2003.
20. Braids and Homotopy Groups, talked at International conference on Homotopy theory and related topics, February 2-5, 2004, Korea; 3-3:45 pm Feb. 3.
21. The Exponent Problem in Homotopy Theory, talked at International conference on Homotopy theory and related topics, February 2-5, 2004, Korea; 3-3:45 pm Feb. 4.
22. Braids and Homotopy Groups, talked at Nankai University, 4-6 pm June 8, 2004.
23. Homotopy Groups, Configuration Spaces and the Braid Groups, talked at Zhejiang University, 9-10 am July 5, 2004.
24. The Exponent Problem and Cohen Groups talked at Department of Mathematics, University of Rochester, 4-5 pm, January 26, 2005.
25. Cohen Groups talked at "International conference on Homotopy theory and related topics, February 1-4, 2005, Korea; Pre-meeting on January 31.
26. Configuration Spaces and the Evaluation Maps talked at "International conference on Homotopy theory and related topics", February 1-4, 2005, Korea. 2:30-3:15 pm, February 1.
27. The Exponent Problem and Cohen Groups talked at Department of Mathematics, MIT, March 28, 2005
28. 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 2-3, 2005.
29. Homotopy groups and Braids talked at Department of Mathematics, Columbia University, April 29, 2005.
30. Representations in classical homotopy theory talked at "Annual Conference on Algebraic Topology", Matsumoto, Japan, July 13-16, 2005.
31. From braid groups to homotopy Groups talked at the Third Pacific Rim Conference on Mathematics, Fudan University, Shanghai, China, August 17?1,2005. (1:30-2:15pm August 17, 2005)
32. The Exponent Problem and Cohen Groups talked at "`Stable and algebraic homotopy", Schloss Ringberg, Germany, October 30-November 5, 2005.
33. Decompositions of loop spaces talked in International Conference on Algebraic Topology, Kyoto, Japan, December 5-8, 2005.
34. Homotopy Groups Talked at NUS Summer School, 9:30-10:30, May 25, 2006.
35. H-spaces with rectractile generating complexes talked in International Conferences on Geometric Topology, Capital Normal University, China, June 16-18, 2006.
36. The functor Amin talked in Topology Conference in honor of the 90th birthday of Professor Zhang Su-Cheng, Institute of Mathematics, Chinese Academy of Sciences, July 10-11, 2006.
37. Braid Groups, 5-hour lectures in the International Summer School on Geometric Topology, Liaoning Normal University, Dalian, China, July 19-28, 2006.
38. EHP-sequences for (p-1)-cell complexes International Conference in Algebraic Topology, Henan University, Kai Feng, Henan, China, October 15-18, 2006.
39. Topology and Poincare Conjecture, Mathematics Enrichment Camp 2006, National University of Singapore, 11:30-12:30 December 14, 2006
40. Simplicial Objects and Homotopy Groups, 4-hour lecture, Program on Braids, Institute of Mathematical Siences, National University of Singapore, 14 May- 13 July, 2007.
41. Mirror Reflections on Braids and the Higher Homotopy Groups of the 2-sphere, talked on June 21, 2007, in Geometric Topology Conference-Beijing 2007, June 18-22, 2007.
42. Adams Spectral Sequences and the Yang-Baxter Lie algebra, talked on July 18, 2007, in Algebraic and Differential Topology Conference at Nankai University, Tianjin, China, July 18-22, 2007.
43. Connections between algebraic topology and the theory of braids, Public Talk of National Science Award 2007 of Singapore, September 20, 2007.
44. Boundary Brunnian braids, mirror reflection and the homotopy groups, talked in 1st East Asia Conference on Algebraic Topology, Seoul National University, Seoul, Korea. November 2-6, 2007
45. Artin braid groups and the homotopy groups--Joint with Jingyan Li talked in International Conference on Topology and its Applications 2007, Kyoto University, December 3-7, A Joint conference with "4th Japan Mexico Topology Conference".
46. Simplicial Structure on Braids and Homotopy Groups, talked in Topology Seminar of Kyushu University on December 10, 2007.
47. Braid Groups and Homotopy Groups II, talked in Topology Seminar of Dalian University of Technology on December 18, 2007.
48. Simplicial Objects, 4-hour talks in Small Algebraic Topology Conference at Fudan University, December 20-23, 2007.
49. Braids, configurations and homotopy groups, talked in Topology Seminar of Hebei Normal University, December 31, 2007.
50. Braid Groups and Homotopy Groups III, talked in Topology Seminar of Dalian University of Technology on January 8, 2008.