HF=HM, V: Seiberg-Witten Floer homology and handle additions
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AbstractThis is the last of five papers [KLT1, KLT2, KLT3, KLT4] that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold. See Theorem 1.4 below for a precise statement. As outlined in [KLT1], this isomorphism is given as a composition of three isomorphisms. In this article, we establish the third isomorphism that relates the Seiberg-Witten Floer homology on the auxiliary manifold with the appropriate version of Seiberg-Witten Floer homology on the original manifold. This constitutes Theorem 4.1 in [KLT1], re-stated in a more refined form as Theorem 1.1 below. The tool used in the proof is a filtered variant of connected sum formula for Seiberg-Witten Floer homology, in special cases where one of the summand manifolds is S1 × S2 (referred to as “handle-addition” in all five articles in this series). Nevertheless, the arguments leading to the afore-mentioned connected sum formula are general enough to establish a connected sum formula in the wider context of Seiberg-Witten Floer homology with non-balanced perturbations. This is stated as Proposition 6.7 below. Although what is asserted in this proposition has been known to experts for some time, a detailed proof has not appeared in the literature, and therefore of some independent interest.
Acceptance Date08/03/2019
All Author(s) ListC. Kutluhan, Y.-J. Lee, C. H. Taubes
Journal nameGeometry and Topology
Volume Number24
Issue Number7
Pages3471 - 3748
LanguagesEnglish-United States

Last updated on 2021-07-12 at 00:40