#### Volume 4, issue 2 (2004)

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 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Heegaard Floer homology of certain mapping tori

### Stanislav Jabuka and Thomas Mark

Algebraic & Geometric Topology 4 (2004) 685–719
 arXiv: math.GT/0405314
##### Abstract

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

##### Keywords
Heegaard Floer homology, mapping tori
Primary: 57R58
Secondary: 53D40