552 - Elementary Geometric and Algebraic Topology
Prerequisites:
Math 551 and 542 or consent of the instructor.
Frequency:
Irregular.
Student Body:
Math majors and graduate students in related areas
Credits:
3. (N-A) Recent Texts:
Essential Topology by M.D. Crossley
Course Coordinator:
Jeff Viaclovsky Background and Goals:
This course is an undergraduate introduction to algebraic topology. Emphasis is placed on geometric aspects.
Alternatives:
N/A
Subsequent Courses:
N/A Course Content:
- Fundamental group and applications: classification of closed 2-manifolds, elementary homotopy theory, the fundamental group of the circle, covering spaces
- Simplicial homology: simplexes, triangulation, homology groups, Euler characteristic, simplicial approximation
- Selected topics: fixed point theorems, singular homology, knot theory, group actions