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On
homology cobordism and local equivalence between plumbed
manifolds
Irving Dai and Matthew Stoffregen |
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Geometry & Topology 23 (2019) 865–924
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Abstract |
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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 is a linear combination of AR plumbed homology spheres with , then is not torsion in the homology cobordism group. A general computation of the involutive Heegaard Floer correction terms for these spaces is also included. |
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Keywords
involutive Heegaard Floer homology, homology cobordism
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Mathematical Subject Classification 2010
Primary: 57R58
Secondary: 57M27
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References |
Publication
Received: 10 December 2017
Revised: 22 July 2018
Accepted: 30 August 2018
Published: 8 April 2019
Proposed: András I Stipsicz
Seconded: Ciprian Manolescu, Walter Neumann
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Authors |
| Irving Dai | |
| Department of Mathematics Princeton University Princeton, NJ United States |
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| Matthew Stoffregen | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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