Heegaard Floer homology of certain mapping tori

Details Heegaard Floer homology of certain mapping tori Heegaard Floer homology of certain mapping tori

2004-05-16

arxiv.org/abs/math/0405314v2

Algebr. Geom. Topol. 4 (2004) 685-719

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-31.abs.html

Scientific paper

We calculate the Heegaard Floer homologies$HF^+(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 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}.

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