MATH 656
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Algebraic Topology
Mathematics
College of Computational, Mathematical, & Physical Sciences
Course Description
A rigorous treatment of the fundamentals of homology and cohomology of spaces: simplicial, singular, and cellular homology; excision; Mayer-Vietoris sequence; homology with coefficients; homology and the fundamental group; universal coefficient theory; cup product; and Poincare Duality.
When Taught
Winter Odd Years
Min
3
Fixed/Max
3
Fixed
3
Fixed
0
Other Prerequisites
Math 553 or equivalent.
Recommended
Math 554
Title
Overview
Learning Outcome
Fundamental group and homotopy
Constructions
Van Kampen Theorem
Covering spaces and group actions
Higher homotopy groups
Homology
Simplicial, singular, cellular
Exact sequences and excision
Mayer-Vietoris sequences
Homology with coefficients
Homology and the fundamental group
Cohomology
Universal coefficient theorem
Cup product
Poincare duality
Title
Learning Outcomes
Learning Outcome
Students should be able to demonstrate mastery of relevant vocabulary, and use the vocabulary fluently in their work. They should know common examples and counterexamples, and be able prove that these examples and counterexamples have properties as claimed. Additionally, students should know the content (and limitations) of major theorems and the ideas of the proofs, and apply results of these theorems to solve suitable problems, or use techniques of the proofs to prove additional related results, or to make calculations and computations. For more detailed information visit the Math 656 Wiki page.
