Computing HF^ by factoring mapping classes
Geometric Topology
2015-02-10 v4 Symplectic Geometry
Abstract
Bordered Heegaard Floer homology is an invariant for three-manifolds with boundary. In particular, this invariant associates to a handle decomposition of a surface F a differential graded algebra, and to an arc slide between two handle decompositions, a bimodule over the two algebras. In this paper, we describe these bimodules for arc slides explicitly, and then use them to give a combinatorial description of HF^ of a closed three-manifold, as well as the bordered Floer homology of any 3-manifold with boundary.
Cite
@article{arxiv.1010.2550,
title = {Computing HF^ by factoring mapping classes},
author = {Robert Lipshitz and Peter S. Ozsváth and Dylan P. Thurston},
journal= {arXiv preprint arXiv:1010.2550},
year = {2015}
}
Comments
106 pages, 46 figures