Seiberg-Witten-Floer stable homotopy type of three-manifolds with b_1=0

  title={Seiberg-Witten-Floer stable homotopy type of three-manifolds with b\_1=0},
  author={Ciprian Manolescu},
  journal={arXiv: Differential Geometry},
Using Furuta's idea of finite dimensional approximation in Seiberg-Witten theory, we refine Seiberg-Witten Floer homology to obtain an invariant of homology 3-spheres which lives in the S^1-equivariant graded suspension category. In particular, this gives a construction of Seiberg-Witten Floer homology that avoids the delicate transversality problems in the standard approach. We also define a relative invariant of four-manifolds with boundary which generalizes the Bauer-Furuta stable homotopy… Expand
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