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

By Ciprian Manolescu. 2001

119 citations recorded by the source corpus.

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 invariant of closed four-manifolds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f19b274b1dcc2527a4e5e65c1d17fb8ef6a1f16d

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Pin(2)-equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture (2013, methodology): “We mention that we chose the methods in [36] because (for rational homology 3-spheres) they seemed easiest from a technical point of view.”
Grid Homology for Knots and Links (2015, methodology): “Note that for Seiberg-Witten theory, and Y a rational homology three-sphere, Manolescu [130] constructed an S(1)-spectrum whose S(1)-equivariant cohomology is monopole Floer homology.”
Floer homology and knot complements (2003, background): “HF(Y ) as being the ordinary homology of a space with an S 1 action, and HF + (Y ) as being its equivariant homology. (See [ 14 ] for a very”