MA 4215, Spring 2000

Introduction to Algebraic Topology



Lecturer: Wu Jie matwuj@nus.edu.sg , Phone: 874-4940.

Office: S14, #04-07, Faculty of Science, Lower Kent Ridge Road.





General information about this module

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.

Assessment

Continuous assessment, consisting of participation at tutorials and one midterm tests during the term, determines 20% of the marks. The final examination determines the remaining 80% of the marks.
NO MAKE-UP TESTS

Final Exam:

Course contents

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.



Lectures


Time-table

DAY TIME VENUE
Tuesday
1-3 pm
S13 04-02
Wednesday
12-2 pm
S13 04-02


Lecture will begin in the week of 3 January 2000.
Lecture Notes

Tutorials
tutorial sheets


Feedback on matters related to the course will be welcome. Please send it to
matwuj@nus.edu.sg