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Reference: Juhász, AI, (2016). Cobordisms of sutured manifolds and the functoriality of link Floer homology. Advances in Mathematics, 299, 940–1038.Citable link to this page:

 

Cobordisms of sutured manifolds and the functoriality of link Floer homology

Abstract: It has been a central open problem in Heegaard Floer theorywhether cobordisms of links induce homomorphisms on the associated linkFloer homology groups. We provide an affirmative answer by introducing anatural notion of cobordism between sutured manifolds, and showing that sucha cobordism induces a map on sutured Floer homology. This map is a commongeneralization of the hat version of the closed 3-manifold cobordism map inHeegaard Floer theory, and the contact gluing map defined by Honda, Kazez,and Mati´c. We show that sutured Floer homology, together with the abovecobordism maps, forms a type of TQFT in the sense of Atiyah. Applied to thesutured manifold cobordism complementary to a decorated link cobordism,our theory gives rise to the desired map on link Floer homology. Hence, linkFloer homology is a categorification of the multi-variable Alexander polynomial.We outline an alternative definition of the contact gluing map usingonly the contact element and handle maps. Finally, we show that a Weinsteinsutured manifold cobordism preserves the contact element.

Publication status:PublishedPeer Review status:Peer reviewedVersion:Accepted Manuscript Funder: Royal Society   Notes:Copyright © 2016 Elsevier Inc. This is the accepted manuscript version of the article. The final version is available online from Elsevier at: https://doi.org/10.1016/j.aim.2016.06.005

Bibliographic Details

Publisher: Elsevier

Publisher Website: http://www.elsevier.com/

Journal: Advances in Mathematicssee more from them

Publication Website: http://www.journals.elsevier.com/advances-in-mathematics

Volume: 299

Extent: 940–1038

Issue Date: 2016

pages:940–1038Identifiers

Urn: uuid:0703d878-43c1-4763-91f5-d0ba1b083b1f

Source identifier: 627178

Eissn: 1090-2082

Issn: 0001-8708

Doi: https://doi.org/10.1016/j.aim.2016.06.005 Item Description

Type: Journal article;

Version: Accepted ManuscriptKeywords: sutured manifold Heegaard Floer homology cobordism Tiny URL: pubs:627178

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Author: Juhász, AI - institutionUniversity of Oxford Oxford, MPLS, Mathematical Institute - - - - Bibliographic Details Publisher: Elsev

Source: https://ora.ox.ac.uk/objects/uuid:0703d878-43c1-4763-91f5-d0ba1b083b1f



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