Heegaard Floer homology of certain mapping tori

Abstract

Abstract. 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 γ and δ be a pair of geometrically dual nonseparating curves on a genus g Riemann surface Σg, and let σ be a curve separating Σg into components of genus 1 and g − 1. Write tγ, tδ, and tσ for the right-handed Dehn twists about each of these curves. The examples we consider are the mapping tori of the diffeomorphisms tm γ ◦tn δ for m, n ∈ Z and that of tn σ, n ∈ Z. 1.