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Variants of equivariant Seiberg-Witten Floer homology


Marcolli, M; Wang, B-L (2005). Variants of equivariant Seiberg-Witten Floer homology. In: Booss-Bavnbek, B; Grubb, G; Wojciechowski, K P. Spectral geometry of manifolds with boundary and decomposition of manifolds. Providence, RI: American Mathematical Society, 225-238.

Abstract

For a rational homology 3-sphere Y with a Spin c structure s, we show that simple algebraic manipulations of our construction of equivariant Seiberg-Witten Floer homology in lead to a collection of variants, which are all topological invariants. We establish a long exact sequence relating them and we show that they satisfy a duality under orientation reversal. We explain their relation to the equivariant Seiberg-Witten Floer (co)homologies introduced in [loc. cit.]. We conjecture the equivalence of these versions of equivariant Seiberg-Witten Floer homology with the Heegaard-Floer invariants introduced by Ozsváth and Szabó.

Abstract

For a rational homology 3-sphere Y with a Spin c structure s, we show that simple algebraic manipulations of our construction of equivariant Seiberg-Witten Floer homology in lead to a collection of variants, which are all topological invariants. We establish a long exact sequence relating them and we show that they satisfy a duality under orientation reversal. We explain their relation to the equivariant Seiberg-Witten Floer (co)homologies introduced in [loc. cit.]. We conjecture the equivalence of these versions of equivariant Seiberg-Witten Floer homology with the Heegaard-Floer invariants introduced by Ozsváth and Szabó.

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Additional indexing

Other titles:Proceedings of the workshop held at Roskilde University, Roskilde, August 6–9, 2003
Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:rational homology 3-sphere, Spin c structure, topological invariants
Language:English
Date:2005
Deposited On:29 Nov 2010 16:26
Last Modified:29 Jul 2020 19:38
Publisher:American Mathematical Society
Series Name:Contemporary Mathematics
Number:366
ISSN:0271-4132
ISBN:0-8218-3536-X
Additional Information:First published in [Contemp. Math., 366, Amer. Math. Soc., Providence, RI, 2005], published by the American Mathematical Society
OA Status:Closed
Official URL:http://www.ams.org/publications/books/monographs/conm-home
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2114490