TOPOLOGY II
MATH 550A--Fall 2009
SCHEDULE:
Tu Th 4:00-5:30 pm LOCATION:
LA5-151 SCHEDULE CODE:
6492
INSTRUCTOR: S. Watson
OFFICE:
FO3-200 OFFICE PHONE: 562-985-5784
OFFICE HOURS: T Th 3:00-3:50 pm and T 6:00- 6:50 pm,
and by appointment
E-MAIL: saleem@csulb.edu
WEBSITE: www.csulb.edu/~saleem
PREREQUISITES: MATH
361B
TEXTBOOK: Algebraic
Topology: An Introduction, by W. S. Massehy, Springer (ISBN: 0387902716)
COURSE CONTENT:
We will study basic concepts in homotopy theory and homology theory for compact manifolds. Homotopy: the fundamental group, Brower's fixed point theorem, homotopy equivalence, free groups and group presentations, Seifert-Van Kampen theorem, topological groups and group actions, covering spaces. Homology: complexes and polyhedra, simplicial homology, Euler-Poncare theorem, simplicial approximation and induced homomorphisms, Brower-Poincare theorem, the Lefschetz fixed-point theorem. The relationship between the fundamental group and the first homotopy group, Cech homology and the invariance of the homology groups.
GRADING: Grades will be based on assignments and in-class presentations.
REFERENCES:
1. F. Croom, Basic Concepts of Algebraic Topology, Springer-Verlag.
2. J. G. Hocking and G. S. Young, Topology, Addison-Wesley.
3. M. A. Armstrong, Basic Topology, Springer-Verlag.
4. Stillwell, Classical Topology and Combinatorial Group Theory, Springer-Verlag.
5. J. Dieudonne, History of Algebraic and Differential Topology 1900-1960,
Springer-Verla