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  • 1
    Publication Date: 2011-05-18
    Description: This research announcement continues the study of the symplectic homology of Weinstein manifolds undertaken by the authors [Bourgeois F, Ekholm T, Eliashberg Y (2009) arXiv:0911.0026] where the symplectic homology, as a vector space, was expressed in terms of the Legendrian homology algebra of the attaching spheres of critical handles. Here, we express the product and Batalin–Vilkovisky operator of symplectic homology in that context.
    Keywords: Low Dimensional Geometry and Topology Special Feature
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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  • 2
    Publication Date: 2011-05-18
    Description: This paper is a companion to the authors’ forthcoming work extending Heegaard Floer theory from closed 3-manifolds to compact 3-manifolds with two boundary components via quilted Floer cohomology. We describe the first interesting case of this theory: the invariants of 3-manifolds bounding , regarded as modules over the Fukaya category of the punctured 2-torus. We extract a short proof of exactness of the Dehn surgery triangle in Heegaard Floer homology. We show that A∞-structures on the graded algebra A formed by the cohomology of two basic objects in the Fukaya category of the punctured 2-torus are governed by just two parameters (m6, m8), extracted from the Hochschild cohomology of A. For the Fukaya category itself, m6 ≠ 0.
    Keywords: Low Dimensional Geometry and Topology Special Feature
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
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