58 research outputs found
Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture
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.Comment: 29 pages; final version, to appear in Journal of the AM
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