Barth, Kilian, Geiges, Hansjorg and Zehmisch, Kai ORCID: 0000-0002-9512-860X (2019). The diffeomorphism type of symplectic fillings. J. Symplectic Geom., 17 (4). S. 929 - 972. SOMERVILLE: INT PRESS BOSTON, INC. ISSN 1540-2347

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Abstract

We show that simply connected contact manifolds that are subcritically Stein fillable have a unique symplectically aspherical filling up to diffeomorphism. Various extensions to manifolds with non-trivial fundamental group are discussed. The proof rests on homological restrictions on symplectic fillings derived from a degree-theoretic analysis of the evaluation map on a suitable moduli space of holomorphic spheres. Applications of this homological result include a proof that compositions of right-handed Dehn twists on Liouville domains are of infinite order in the symplectomorphism group. We also derive uniqueness results for subcritical Stein fillings up to homotopy equivalence and, under some topological assumptions on the contact manifold, up to diffeomorphism or symplectomorphism.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Barth, KilianUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Geiges, HansjorgUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Zehmisch, KaiUNSPECIFIEDorcid.org/0000-0002-9512-860XUNSPECIFIED
URN: urn:nbn:de:hbz:38-160440
DOI: 10.4310/JSG.2019.v17.n4.a1
Journal or Publication Title: J. Symplectic Geom.
Volume: 17
Number: 4
Page Range: S. 929 - 972
Date: 2019
Publisher: INT PRESS BOSTON, INC
Place of Publication: SOMERVILLE
ISSN: 1540-2347
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
RABINOWITZ FLOER HOMOLOGY; CONTACT STRUCTURES; OPEN BOOKS; MANIFOLDS; RIGIDITY; TOPOLOGYMultiple languages
MathematicsMultiple languages
Refereed: Yes
URI: http://kups.ub.uni-koeln.de/id/eprint/16044

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