Heegaard Floer homology of certain mapping tori

Jabuka, Stanislav; Mark, Thomas E

doi:10.2140/agt.2004.4.685

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Heegaard Floer homology of certain mapping tori

Stanislav Jabuka and Thomas Mark

Algebraic & Geometric Topology 4 (2004) 685–719

DOI: 10.2140/agt.2004.4.685

arXiv: math.GT/0405314

Abstract

We calculate the Heegaard Floer homologies $H F^{+} (M, s)$ for mapping tori $M$ associated to certain surface diffeomorphisms, where $s$ is any ${spin}^{c}$ structure on $M$ whose first Chern class is non-torsion. Let $γ$ and $δ$ be a pair of geometrically dual nonseparating curves on a genus $g$ Riemann surface $Σ_{g}$ , and let $σ$ be a curve separating $Σ_{g}$ into components of genus $1$ and $g - 1$ . Write $t_{γ}$ , $t_{δ}$ , and $t_{σ}$ for the right-handed Dehn twists about each of these curves. The examples we consider are the mapping tori of the diffeomorphisms $t_{γ}^{m} \circ t_{δ}^{n}$ for $m, n \in ℤ$ and that of $t_{σ}^{\pm 1}$ .

Keywords

Heegaard Floer homology, mapping tori

Mathematical Subject Classification 2000

Primary: 57R58

Secondary: 53D40

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Publication

Received: 6 July 2004

Accepted: 16 August 2004

Published: 9 September 2004

Authors

Stanislav Jabuka
Department of Mathematics Columbia University 2990 Broadway New York NY 10027 USA

Thomas Mark
Department of Mathematics Southeastern Louisiana University 1205 North Oak Street Hammond LA 70402 USA

Volume 4, issue 2 (2004)