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

  title={Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture},
  author={Ciprian Manolescu},
  journal={arXiv: Geometric Topology},
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… Expand
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