Computing HF by factoring mapping classes

Robert Lipshitz, Peter S. Ozsváth, Dylan P. Thurston

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

Bordered Heegaard Floer homology is an invariant for 3-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 3-manifold, as well as the bordered Floer homology of any 3-manifold with boundary.

Original languageEnglish (US)
Pages (from-to)2547-2681
Number of pages135
JournalGeometry and Topology
Volume18
Issue number5
DOIs
StatePublished - Dec 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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