#### Volume 19, issue 5 (2019)

 Recent Issues
Author Index
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 To Appear Other MSP Journals
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 $\iota$–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