MATH 225C

Main Course

Algebraic Topology

Description

Lecture, three hours; discussion, one hour. Homotopy theory: fundamental group, covering spaces, Van Kampen's theorem. Homology theory: singular homology, simplicial homology, homotopy invariance, relative homology, excision and Mayer-Vietoris, functoriality, relationship to the fundamental group, calculations with cellular complexes (CW complexes). Cohomology theory: singular cohomology, universal coefficient theorem, cup products. S/U or letter grading.