# Computations of Instanton Knot Floer Homology with Local Coefficients

## [HYBRID WORKSHOP] New Four-Dimensional Gauge Theories October 24, 2022 - October 28, 2022

**Speaker(s):**Tomasz Mrowka (Massachusetts Institute of Technology)

**Location:**SLMath: Eisenbud Auditorium, Online/Virtual

**Tags/Keywords**

Instaton Floer homology

**Primary Mathematics Subject Classification**

**Secondary Mathematics Subject Classification**

Instanton knot Floer homology admits an interesting deformation (unavailable without the knot). The deformation is a Floer homology with local coefficients. Though more complicated than the vanilla version they turn out to be easier to compute. We’ll describe some of computations of these modules. A key computation is the trivial n-strand braid in S1xS2, generalizing work of Ethan Street. This is joint work with Peter Kronheimer.