Floer homology of 3-manifolds with torus boundary
Jacob Rasmussen
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, United Kingdom
![Floer homology of 3-manifolds with torus boundary cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fbooks%2Fcover-276.png&w=3840&q=90)
This book chapter is published open access.
Abstract
Manifolds with torus boundary have played a special role in the study of Floer homology for 3-manifolds since the early days of the subject. In joint work with Jonathan Hanselman and Liam Watson, we defined a geometrical Heegaard Floer invariant for 3-manifolds with torus boundary. The invariant is a reformulation of the bordered Floer homology of Lipshitz, Ozsváth, and Thurston, and takes the form of a collection of immersed closed curves (possibly decorated with local systems) in a covering space of the punctured torus. We briefly discuss the construction of the invariant and some applications to the L-space conjecture of Boyer–Gordon–Watson and Juhász. We then describe a generalization to manifolds with sutured boundary, and some applications to the study of satellite knots.