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Equivariant Seiberg-Witten Floer homology

Marcolli, Matilde and Wang, Bai-Ling (2001) Equivariant Seiberg-Witten Floer homology. Communications in Analysis and Geometry, 9 (3). pp. 451-639. ISSN 1019-8385. doi:10.4310/CAG.2001.v9.n3.a1.

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In this paper we construct, for all compact oriented three- manifolds, a U(1)-equivariant version of Seiberg-Witten Floer homology, which is invariant under the choice of metric and perturbation. We give a detailed analysis of the boundary structure of the monopole moduli spaces, compactified to smooth manifolds with corners. The proof of the independence of metric and perturbation is then obtained via an analysis of all the relevant obstruction bundles and sections, and the corresponding gluing theorems. The paper also contains a discussion of the chamber structure for the Seiberg-Witten invariant for rational homology 3-spheres, and proofs of the wall crossing formula, obtained by studying the exact sequences relating the equivariant and the non-equivariant Floer homologies and by a local model at the reducible monopole.

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Additional Information:© 1997 International Press. Received June 13, 1997. We are deeply grateful to T. Mrowka for the many invaluable comments and suggestions. We thank A. Carey and M. Rothenberg for the many useful conversations. We are grateful to L. Nicolaescu for useful remarks and suggestions. In the early stages of this work useful were comments of R. Brussee, G. Matic, R. Mazzeo, J.W. Morgan, and R.G. Wang. We thank the referee for the very detailed and useful comments and for many valuable suggestions on how to improve various sections of the manuscript. Parts of this work were carried out during visits of the two authors to the Max Planck Institut für Mathematik in Bonn, and visits of the first author to the University of Adelaide and to the Tata Institute of Fundamental Research. We thank these institutions for the kind hospitality and for support. The first author was partially supported by NSF grant DMS-9802480. The second author was supported by ARC fellowship.
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ID Code:27626
Deposited By: Tony Diaz
Deposited On:04 Nov 2011 20:21
Last Modified:09 Nov 2021 16:50

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