Connected Heegaard Floer homology of sums of Seifert fibrations

Dai, Irving

doi:10.2140/agt.2019.19.2535

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Connected Heegaard Floer homology of sums of Seifert fibrations

Irving Dai

Algebraic & Geometric Topology 19 (2019) 2535–2574

DOI: 10.2140/agt.2019.19.2535

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

Volume 19, issue 5 (2019)