Introduction to Algebraic Topology

Graduate / Professional

This is a one-term graduate introductory course in algebraic topology. We discuss algebraic and combinatorial tools used by topologists to encode information about topological spaces. Broadly speaking, we study the fundamental group of a space, its homology, and its cohomology. While focusing on the basic properties of these invariants, methods of computation, and many examples, we also see applications toward proving classical results. These include the Brouwer fixed-point theorem, the Jordan curve theorem, Poincaré duality, and others. The main text is Allen Hatcher’s Algebraic Topology, which is available for free on his website. Prerequisites: Linear algebra ( MATH 2250 or 2260 ), Analysis 1 ( MATH 2550 or 2560 ), abstract algebra ( MATH 3500 ) required. Topology (MATH 430) is strongly recommended, and much of the material is assumed. Analysis 2 ( MATH 3020 ) is recommended. MW 2:35pm-3:50pm