Geometry & Topology
- Geom. Topol.
- Volume 23, Number 2 (2019), 865-924.
On homology cobordism and local equivalence between plumbed manifolds
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.
Geom. Topol., Volume 23, Number 2 (2019), 865-924.
Received: 10 December 2017
Revised: 22 July 2018
Accepted: 30 August 2018
First available in Project Euclid: 17 April 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Dai, Irving; Stoffregen, Matthew. On homology cobordism and local equivalence between plumbed manifolds. Geom. Topol. 23 (2019), no. 2, 865--924. doi:10.2140/gt.2019.23.865. https://projecteuclid.org/euclid.gt/1555466432