On homology cobordism and local equivalence between plumbed manifolds

Abstract

We establish a structural understanding of the involutive Heegaard Floer homology for all linear combinations of almost-rational (AR) plumbed three-manifolds. We use this to show that the Neumann-Siebenmann invariant is a homology cobordism invariant for all linear combinations of AR plumbed homology spheres. As a corollary, we prove that if $Y$ is a linear combination of AR plumbed homology spheres with $\mu (Y)=1$, then $Y$ is not torsion in the homology cobordism group. A general computation of the involutive Heegaard Floer correction terms for these spaces is also included.

43 pages; final version, to appear in Geometry & Topology

References in corpus (3)

• Involutive Heegaard Floer homology
• A splitting theorem for the Seiberg-Witten invariant of a homology $S^1\times S^3$
• Manolescu Invariants of Connected Sums

Cited by in corpus (4)

• A survey of the homology cobordism group
• Almost simple linear graphs, homology cobordism and connected Heegaard Floer homology
• Ozsvath-Szabo $d$-invariants of almost simple linear graphs
• Connected Heegaard Floer homology of sums of Seifert fibrations