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Fiber Floer cohomology and conormal stops
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Let S be a closed orientable spin manifold. Let K⊂S be a submanifold and denote its complement by MK. In this paper we prove that there exists an isomorphism between partially wrapped Floer cochains of a cotangent fiber stopped by the unit conormal ΛK and chains of a Morse theoretic model of the based loop space of MK, which intertwines the A∞-structure with the Pontryagin product. As an application, we restrict to codimension 2 spheres K⊂Sn where n=5 or n≥7. Then we show that there is a family of knots K so that the partially wrapped Floer cohomology of a cotangent fiber is related to the Alexander invariant of K. A consequence of this relation is that ΛK is not Legendrian isotopic to Λunknot.

National Category
Geometry
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-403151OAI: oai:DiVA.org:uu-403151DiVA, id: diva2:1388346
Available from: 2020-01-24 Created: 2020-01-24 Last updated: 2020-01-29Bibliographically approved
In thesis
1. Fiber Floer cohomology and conormal stops
Open this publication in new window or tab >>Fiber Floer cohomology and conormal stops
2020 (English)Licentiate thesis, monograph (Other academic)
Place, publisher, year, edition, pages
Uppsala: Uppsala universitet, 2020. p. 53
Series
U.U.D.M. report / Uppsala University, Department of Mathematics, ISSN 1101-3591 ; 1
National Category
Geometry
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-403462 (URN)
Presentation
2020-02-04, sal 80127, Ångströmlaboratoriet, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2020-01-30 Created: 2020-01-29 Last updated: 2020-01-30Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
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  • Other style
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Language
  • de-DE
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  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
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