HF=HM V: Seiberg-Witten-Floer homology and handle addition
Cagatay Kutluhan, Yi-Jen Lee, Cliff H. Taubes
TL;DR
This paper completes a series establishing an isomorphism between Seiberg-Witten Floer homology and Heegaard Floer homology for 3-manifolds, advancing the understanding of their equivalence.
Contribution
It finalizes the proof of the isomorphism between Seiberg-Witten Floer homology and Heegaard Floer homology for compact, oriented 3-manifolds.
Findings
Confirmed the isomorphism between the two homologies.
Provided new techniques for handle addition in Floer homology.
Unified different Floer homology theories for 3-manifolds.
Abstract
This is the last of five papers that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics