Algebraic & Geometric Topology

Connected Heegaard Floer homology of sums of Seifert fibrations

Irving Dai

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

homology cobordism involutive Heegaard Floer homology connected Heegaard Floer homology


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.

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