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Apr 25, 2024
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MATH 6710 - Algebraic Topology
The fundamental group and the van Kampen theorem, homology of complexes, exact sequences, polyhedra and CW-complexes, simplicial and singular homology and cohomology, applications to Euclidean spaces (the Jordan theorem, the Brouwer fixed point theorem, topological invariance of open sets), covering spaces, fibrations and cofibrations, higher homotopy groups, manifolds and Poincare duality, characteristic classes of vector bundles, introduction to K-theory.
Requisites: MATH 6700
Credit Hours: 4
Repeat/Retake Information: May not be retaken.
Lecture/Lab Hours: 3.0 lecture
Grades: Eligible Grades: A-F,WP,WF,WN,FN,AU,I
Learning Outcomes:
- Apply the fixed point theorem and its variations to problems in other areas of mathematics.
- Calculate homology and cohomology groups of spheres, tori, real and complex projective spaces, and other manifolds.
- Recognize geometric problems that can be solved using methods of algebraic topology.
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