Algebraic & Geometric Topology

Connected Heegaard Floer homology of sums of Seifert fibrations

Irving Dai

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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.

Article information

Source
Algebr. Geom. Topol., Volume 19, Number 5 (2019), 2535-2574.

Dates
Received: 4 May 2018
Revised: 8 October 2018
Accepted: 30 October 2018
First available in Project Euclid: 26 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.agt/1572055267

Digital Object Identifier
doi:10.2140/agt.2019.19.2535

Mathematical Reviews number (MathSciNet)
MR4023322

Zentralblatt MATH identifier
07142612

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds 57R58: Floer homology

Keywords
homology cobordism involutive Heegaard Floer homology connected Heegaard Floer homology

Citation

Dai, Irving. Connected Heegaard Floer homology of sums of Seifert fibrations. Algebr. Geom. Topol. 19 (2019), no. 5, 2535--2574. doi:10.2140/agt.2019.19.2535. https://projecteuclid.org/euclid.agt/1572055267


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References

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