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Fukaya-Floer homology of Σ×S1 and applications.

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Muñoz, Vicente (1999) Fukaya-Floer homology of Σ×S1 and applications. Journal of Differential Geometry, 53 (2). pp. 279-326. ISSN 0022-040X

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Official URL: http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.jdg/1214425537


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Abstract

We determine the Fukaya-Floer (co)homology groups of the three-manifold y = S x S 1 , where S is a Riemann surface of genus g > 1. These are of two kinds. For the 1-cycle S1 C Y, we compute the Fukaya-Floer cohomology HFF*(Y, S1) and its ring structure, which is a sort of deformation of the
Floer cohomology HF*(Y). On the other hand, for 1-cycles ö C 'S CY, we determine the Fukaya-Floer homology HFF*(Y,S) and its i?-F*(Y)-module structure.
We give the following applications: We show that every four-manifold with 6+ > 1 is of finite type.
Four-manifolds which arise as connected sums along surfaces of fourmanifolds with 6i = 0 are of simple type and we give constraints on their basic classes.
We find the invariants of the product of two Riemann surfaces both of genus greater than or equal to one.


Item Type:Article
Uncontrolled Keywords:Fukaya-Floer homology; Floer homology; 4-manifolds; Donaldson invariants; Simple type.
Subjects:Sciences > Mathematics > Topology
ID Code:21289
Deposited On:10 May 2013 10:40
Last Modified:12 Mar 2019 17:43

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