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Topology II -- Spring 2014
MTH 631 - Topology II. First course in algebraic topology. Homotopy, fundamental group, simplicial homology. PR: MTH550 and MTh630. 3 hours.
- Time and Place: 12:30 pm - 1:45 pm TR 263 Smith Hall.
- Instructor: Peter Saveliev (call me Peter)
- Office: Smith Hall 325
- Office Hours: MW 2:30 - 4:30, or by appointment
- Office Phone: x4639
- E-mail: saveliev@marshall.edu
- Class Web-Page: math02.com
- Prerequisites: Topology I -- Fall 2013
- Text: Topology Illustrated (online draft), specific chapters linked below
- Goals: Introduction to point-set and algebraic topology
- Grade Breakdown:
- homework and quizzes: 40%
- midterm: 25%
- final exam: 35%
- Letter Grades: A: 90-100, B: 80-89, C: 70-79, D: 60-69, F: <60
See also Course policy.
Lectures
They will appear here as the course progresses.
A better organized version of the content of the lectures appears in one of the chapters below within a week. The most current material is marked with $\star$.
Chapters
This is the text that will be followed. The chapters will be updated or rewritten, sometimes significantly, as the course progresses. Read them.
Chapter 4. Topological spaces
Chapter 5. Maps
- Homotopy
- Cell maps
- Homology theory $\star$
- Euler and Lefschetz numbers
- Homology of parametric complexes
Chapter 6. Advanced topics
- Short overview
- Singular complexes
- Homology as a group
- Properties of homology groups
- Spaces vs subspaces: relative homology
- Exact sequences
- Cochain complexes and cohomology
- Homology vs homology of the complement: Alexander duality
- Homology vs cohomology in manifolds: Poincare duality
- Cup product and cap product
- Appendices:
- Commutative diagrams
- Computing homology
- Fundamental group
- Homology and algebra
- Homology as a vector space
- More about manifolds
- Mobius band
Notes
- Topology II -- Spring 2014 -- midterm: March.
- Topology II -- Spring 2014 -- final exam: Tuesday, May 6, 12:45-2:45. Note: If the two-hour time allowance results in a conflict in exam times, it is the student’s responsibility to notify the professor of the later course and to reschedule the later exam.
Related texts: