Bordered Heegaard Floer homology and graph manifolds

Hanselman, Jonathan

doi:10.2140/agt.2016.16.3103

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Bordered Heegaard Floer homology and graph manifolds

Jonathan Hanselman

Algebraic & Geometric Topology 16 (2016) 3103–3166

DOI: 10.2140/agt.2016.16.3103

Abstract

We perform two explicit computations of bordered Heegaard Floer invariants. The first is the type $D$ trimodule associated to the trivial $S^{1}$ –bundle over the pair of pants $P$ . The second is a bimodule that is necessary for self-gluing when two torus boundary components of a bordered manifold are glued to each other. Using the results of these two computations, we describe an algorithm for computing $\hat{H F}$ of any graph manifold.

Keywords

Heegaard Floer homology, bordered Floer homology, graph manifolds

Mathematical Subject Classification 2010

Primary: 57M27, 57R58

References

Publication

Received: 22 November 2013

Revised: 12 January 2016

Accepted: 27 February 2016

Published: 15 December 2016

Authors

Jonathan Hanselman
Department of Mathematics University of Texas at Austin 1 University Station, C1200 Austin, TX 78712 United States

Volume 16, issue 6 (2016)