Floer homology via semi-infinite dimensional cycles

Abstract: Floer's idea of constructing a Morse-Smale-Witten chain complex to compute the "middle-dimensional homology" of infinite-dimensional spaces led to the emergence of groundbreaking invariants of knots, low-dimensional manifolds and symplectic manifolds, collectively known under the name of Floer homology. I will describe a construction of a homological invariant of infinite-dimensional spaces with a functional facilitating what Atiyah called "semi-infinite dimensional cycles", following the work of Lipyanskiy and based on earlier work of Mrowka and Ozsváth. The construction reduces the analytical difficulties needed to define Floer homology and hopefully will provide a convenient framework for constructing equivariant Floer homologies.

geometric topology

Audience: researchers in the topic

Knot theory seminar in Warsaw

Series comments: Description: Research seminar on knot theory

The zoom link is available on the seminar webpage.

Meeting ID: 846 2302 8036, Password: the last name of the first-named author of this fundamental paper on knot theory: Holomorphic disks and topological invariants for closed three-manifolds.