Volume 19, issue 5 (2019)

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Connected Heegaard Floer homology of sums of Seifert fibrations

Irving Dai

Algebraic & Geometric Topology 19 (2019) 2535–2574
Abstract

We compute the connected Heegaard Floer homology (defined by Hendricks, Hom, and Lidman) for a large class of 3–manifolds, including all linear combinations of Seifert fibered homology spheres. We show that for such manifolds, the connected Floer homology completely determines the local equivalence class of the associated ι–complex. Some identities relating the rank of the connected Floer homology to the Rokhlin invariant and the Neumann–Siebenmann invariant are also derived. Our computations are based on combinatorial models inspired by the work of Némethi on lattice homology.

Keywords
homology cobordism, involutive Heegaard Floer homology, connected Heegaard Floer homology
Mathematical Subject Classification 2010
Primary: 57M27, 57R58
References
Publication
Received: 4 May 2018
Revised: 8 October 2018
Accepted: 30 October 2018
Published: 20 October 2019
Authors
Irving Dai
Department of Mathematics
Princeton University
Princeton, NJ
United States