Notes & Miscellanea

Notes on Khovanov homology is an unknot detector  Notes on the famous paper of Kronheimer & Mrowka.

Floer homotopy type following Cohen, Jones and Segal  Slides from a talk where I explained Cohen, Jones and Segal's original definition of Floer homotopy type, they also contain a detailed example in the case of Hamiltonian Floer homology.

Equivariant cohomology, torus actions and 12-24 theorem. These notes originated from trying to understand this paper by Godinho, von Heymann and Sabatini. They contain an introduction to toric actions on symplectic manifolds, Equivariant cohomology and the localization formula.

Regular neighbourhood of embedded simplicial complexes  In studying surgery theory, there is a point when one wants to embed a simplicial complex in R^n and consider a tubular neighbourhood of it which is a smooth manifold with boundary.  In this notes I reprove this well known fact. Note that simplicial complexes have singularities in general so we cannot just apply the classical tubular neighbourhood theorem.