On homology cobordism and local equivalence between plumbed manifolds

Dai, Irving¹ ; Stoffregen, Matthew²

¹ Department of Mathematics, Princeton University, Princeton, NJ, United States
² Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, United States

Geometry & topology, Tome 23 (2019) no. 2, pp. 865-924.

Résumé

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 $\mu \left(Y\right)=1$, 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.

Détail

DOI : 10.2140/gt.2019.23.865

Classification : 57R58, 57M27
Keywords: involutive Heegaard Floer homology, homology cobordism

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