### An introduction to Morse theory and Morse homology

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, September 20, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Akash Narayanan – Georgia Institute of Technology – anarayanan64@gatech.edu

Morse theory analyzes the topology of a smooth manifold by studying the behavior of its real-valued functions. From this, one obtains a well-behaved homology theory which provides further information about the manifold and places constraints on the smooth functions it admits. This idea has proven to be useful in approaching topological problems, playing an essential role in Smale's solution to the generalized Poincare conjecture in dimensions greater than 4. Morse theory has been adapted to study complex manifolds, and even algebraic varieties over more general fields, but the underlying principles remain the same. In this talk, we will define the basic notions of Morse theory and describe some of the fundamental results. Then we will define Morse homology and discuss some important corollaries and applications.