Completed Symplectic Cohomology and Liouville Cobordisms
Symplectic cohomology is an algebraic invariant of filled symplectic cobordisms that encodes dynamical information. In this thesis we define a modified symplectic cohomology theory, called action-completed symplectic cohomology, that exhibits quantitative behavior. We illustrate the non-trivial na...
Main Author: | |
---|---|
Language: | English |
Published: |
2018
|
Subjects: | |
Online Access: | https://doi.org/10.7916/D8FJ3ZWZ |
id |
ndltd-columbia.edu-oai-academiccommons.columbia.edu-10.7916-D8FJ3ZWZ |
---|---|
record_format |
oai_dc |
spelling |
ndltd-columbia.edu-oai-academiccommons.columbia.edu-10.7916-D8FJ3ZWZ2019-05-09T15:15:45ZCompleted Symplectic Cohomology and Liouville CobordismsVenkatesh, Saraswathi2018ThesesMathematicsCohomology operationsSymplectic groupsCobordism theoryInvariantsSymplectic cohomology is an algebraic invariant of filled symplectic cobordisms that encodes dynamical information. In this thesis we define a modified symplectic cohomology theory, called action-completed symplectic cohomology, that exhibits quantitative behavior. We illustrate the non-trivial nature of this invariant by computing it for annulus subbundles of line bundles over complex projective space. The proof relies on understanding the symplectic cohomology of the complex fibers and the quantum cohomology of the projective base. We connect this result to mirror symmetry and prove a non-vanishing result in the presence of Lagrangian submanifolds with non-vanishing Floer homology. The proof uses Lagrangian quantum cohomology in conjunction with a closed-open map.Englishhttps://doi.org/10.7916/D8FJ3ZWZ |
collection |
NDLTD |
language |
English |
sources |
NDLTD |
topic |
Mathematics Cohomology operations Symplectic groups Cobordism theory Invariants |
spellingShingle |
Mathematics Cohomology operations Symplectic groups Cobordism theory Invariants Venkatesh, Saraswathi Completed Symplectic Cohomology and Liouville Cobordisms |
description |
Symplectic cohomology is an algebraic invariant of filled symplectic cobordisms that encodes dynamical information. In this thesis we define a modified symplectic cohomology theory, called action-completed symplectic cohomology, that exhibits quantitative behavior. We illustrate the non-trivial nature of this invariant by computing it for annulus subbundles of line bundles over complex projective space. The proof relies on understanding the symplectic cohomology of the complex fibers and the quantum cohomology of the projective base. We connect this result to mirror symmetry and prove a non-vanishing result in the presence of Lagrangian submanifolds with non-vanishing Floer homology. The proof uses Lagrangian quantum cohomology in conjunction with a closed-open map. |
author |
Venkatesh, Saraswathi |
author_facet |
Venkatesh, Saraswathi |
author_sort |
Venkatesh, Saraswathi |
title |
Completed Symplectic Cohomology and Liouville Cobordisms |
title_short |
Completed Symplectic Cohomology and Liouville Cobordisms |
title_full |
Completed Symplectic Cohomology and Liouville Cobordisms |
title_fullStr |
Completed Symplectic Cohomology and Liouville Cobordisms |
title_full_unstemmed |
Completed Symplectic Cohomology and Liouville Cobordisms |
title_sort |
completed symplectic cohomology and liouville cobordisms |
publishDate |
2018 |
url |
https://doi.org/10.7916/D8FJ3ZWZ |
work_keys_str_mv |
AT venkateshsaraswathi completedsymplecticcohomologyandliouvillecobordisms |
_version_ |
1719046869519171584 |