MAT 645: Topics in Differential Geometry: Floer Homotopy Theory

Course Instructor: Mark McLean (mark.mclean AT stonybrook.edu)

MAT 645 Tuesday, Thursday 9:30am-10:50am, Physics P127.

Introduction to the Course

Cohen Jones and Segal in 1994 explained how one can recover the stable homotopy type of a closed manifold from its Morse function. More recently this has been done in Floer theory in various contexts. In this course we will explain these ideas, starting with the Morse homotopy type and working our way to the Hamiltonian Floer homotopy type.

Prerequisites

Algebraic Topology: MAT541.
Symplectic Geometry: MAT562.
Riemannian Geometry MAT568 is helpful.

Office Hours (Math 3-112) :

Monday 10:30-11:30am
Tuesday 11am-12pm

Suggested Reading

Hutchings: Lecture notes on Morse homology (with an eye towards Floer theory (online).

Audin Damian: Morse Theory and Floer Homology.

Bordism of flow modules and exact Lagrangians by Noah Porcelli and Ivan Smith

Foundation of Floer homotopy theory I: Flow categories by Mohammed Abouzaid and Andrew Blumberg

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