Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture

2013/03/10 by Manolescu, Ciprian · 5 citations
#57M27 #57Q15 #57R58 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1303.2354

Abstract

We define Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres equipped with a spin structure. The analogue of Froyshov's correction term in this setting is an integer-valued invariant of homology cobordism whose mod 2 reduction is the Rokhlin invariant. As an application, we show that there are no homology 3-spheres Y of Rokhlin invariant one such that Y # Y bounds an acyclic smooth 4-manifold. By previous work of Galewski-Stern and Matumoto, this implies the existence of non-triangulable high-dimensional manifolds.

Cited by

• Non-kinetic homotopy coherent actions on four-manifolds
• Homology cobordism for some Sol manifolds
• Homotopy Theory for Ordered Simplicial Complexes
• Universal topological statistics on triangulated singular spaces
• On homology spheres of the trivial local equivalence class

Related

• Lectures on the triangulation conjecture
• Variants of equivariant Seiberg-Witten Floer homology
• The equivalence of two Pin(2)-equivariant Seiberg-Witten Floer homologies
• Homology cobordism and triangulations
• Equivariant and Bott-type Seiberg-Witten Floer Homology: Part II