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MA 4215, Spring 2001
Introduction to Algebraic Topology
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Lecturer: Wu Jie
matwuj@nus.edu.sg , Phone: 874-4940.
Office: S14, #04-07, Faculty of Science, Lower Kent
Ridge Road.
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Prerequisites:MA3213 (#) or MA3251
You should consult the academic advisors on matters related to selection
of modules. The
academic advisors of level 4000 mathematics
modules are A/P A/P Choi Kwok Pui and A/P Fred Leung Pui Fai.
Continuous assessment, consisting of participation at tutorials and one
midterm test during the term, determines 20% of the marks. The final
examination determines the remaining 80% of the marks.
NO MAKE-UP TESTS
Final Exam: 26-APR-2001;
Exam Session: PM;
Exam Venue: NAV.
Review of metric and topological spaces. Constructions and universal
properties, product space, subspace and quotient space, collapsing, smash
product and orbit spaces. Locally compact Hausdorff spaces and
identification maps, compact-open topology.
Paths, path-related points, path-components. Path-equivalence of paths,
the fundamental group and groupoid, change of basepoint, change of space.
Homotopy, simply-connected and contractible spaces, simple-connectedness
of Sn . Homotopy invariance of fundamental group. Covering
spaces,
properly discontinuous group actions. Lifting theorems. Applications,
including Fundamental Theorem of Algebra, Borsuk-Ulam Theorem.
Properly discontinuous actions and classification of covering spaces.
Time-table
| DAY | TIME |
VENUE |
| Tuesday | 4-6 pm
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S13 05-02 |
| Wednesday | 10-12 am
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S13 05-01 |
Lecture will begin in the week of 3 January 2001.
Lecture
Notes
Tutorials
tutorial sheets
Feedback on matters related to the course will be welcome. Please send
it to
matwuj@nus.edu.sg