On the intersection forms of spin four-manifolds with boundary

2013/05/20 by Ciprian Manolescu, Manolescu, Ciprian · 3 citations
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1305.4667

Abstract

We prove Furuta-type bounds for the intersection forms of spin cobordisms between homology 3-spheres. The bounds are in terms of a new numerical invariant of homology spheres, obtained from Pin(2)-equivariant Seiberg-Witten Floer K-theory. In the process we introduce the notion of a Floer K_G-split homology sphere; this concept may be useful in an approach to the 11/8 conjecture.

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• Non-kinetic homotopy coherent actions on four-manifolds
• The Boundary Dehn Twist on a Punctured Connected Sum of Two K3 Surfaces is Nontrivial in the Smooth Mapping Class Group
• On homology spheres of the trivial local equivalence class

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• Constraints on intersection forms of spin 4-manifolds bounded by Seifert rational homology 3-spheres in terms of μ and κ invariants
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• Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture
• Intersection Forms of Spin 4-Manifolds and the Pin(2)-Equivariant Mahowald Invariant
• Involutions, links, and Floer cohomologies