TY - JOUR
T1 - Computing HF by factoring mapping classes
AU - Lipshitz, Robert
AU - Ozsváth, Peter S.
AU - Thurston, Dylan P.
N1 - Publisher Copyright: © 2014, Mathematical Sciences Publishers. All rights reserved
PY - 2014/12/1
Y1 - 2014/12/1
N2 - 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.
AB - 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.
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U2 - https://doi.org/10.2140/gt.2014.18.2547
DO - https://doi.org/10.2140/gt.2014.18.2547
M3 - Article
VL - 18
SP - 2547
EP - 2681
JO - Geometry and Topology
JF - Geometry and Topology
SN - 1465-3060
IS - 5
ER -