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

@article{Manolescu2001SeibergWittenFloerSH,
  title={Seiberg-Witten-Floer stable homotopy type of three-manifolds with b\_1=0},
  author={Ciprian Manolescu},
  journal={arXiv: Differential Geometry},
  year={2001}
}
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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References

SHOWING 1-10 OF 49 REFERENCES
Floer's infinite dimensional Morse theory and homotopy theory
This paper is a progress report on our efforts to understand the homotopy theory underlying Floer homology. Its objectives are as follows: (A) to describe some of our ideas concerning whatExpand
A stable cohomotopy refinement of Seiberg-Witten invariants: I
The monopole map defines an element in an equivariant stable cohomotopy group refining the Seiberg-Witten invariant. Part I discusses the definition of this stable homotopy invariant and its relationExpand
Equivariant Seiberg-Witten Floer Homology
This paper circulated previously in a draft version. Now, upon general request, it is about time to distribute the more detailed (and much longer) version. The main technical issues revolve aroundExpand
Equivariant Stable Homotopy Theory
The last decade has seen a great deal of activity in this area. The chapter provides a brief sketch of the basic concepts of space-level equivariant homotopy theory. It also provides an introductionExpand
The Seiberg-Witten equations and four-manifolds with boundary
An early result by Donaldson says that if Z is closed and JZ is negative definite then JZ is isomorphic to some diagonal form 〈−1〉 ⊕ · · · ⊕ 〈−1〉. More generally one may ask which negative definiteExpand
Poincaré-Lefschetz duality for the homology Conley index
The Conley index for continuous dynamical systems is defined for (one-sided) semiflows. For (two-sided) flows, there are two indices defined: one for the forward flow; and one for the reverse flow.Expand
A refinement of the Conley index and an application to the stability of hyperbolic invariant sets
A compact and isolated invariant set of a continuous flow possesses a so called Conley index, which is the homotopy type of a pointed compact space. For this index a well known continuation propertyExpand
Notes on Seiberg-Witten Theory
Preliminaries The Seiberg-Witten invariants Seiberg-Witten equations on complex surfaces Gluing techniques Epilogue Bibliography Index.
4-manifolds and Kirby calculus
4-manifolds: Introduction Surfaces in 4-manifolds Complex surfaces Kirby calculus: Handelbodies and Kirby diagrams Kirby calculus More examples Applications: Branched covers and resolutions EllipticExpand
The Genus of Embedded Surfaces in the Projective Plane
1. Statement of the result The genus of a smooth algebraic curve of degree d in CP is given by the formula g = (d − 1)(d − 2)/2. A conjecture sometimes attributed to Thom states that the genus of theExpand
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