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Some Classification Results for Symplectic Fillings of Contact 3-Manifolds.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Some Classification Results for Symplectic Fillings of Contact 3-Manifolds./
Author:	Christian, Austin.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	143 p.
Notes:	Source: Dissertations Abstracts International, Volume: 83-01, Section: B.
Contained By:	Dissertations Abstracts International83-01B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28544134
ISBN:	9798516079566

Some Classification Results for Symplectic Fillings of Contact 3-Manifolds.
Christian, Austin.

Some Classification Results for Symplectic Fillings of Contact 3-Manifolds. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 143 p.

Source: Dissertations Abstracts International, Volume: 83-01, Section: B.

Thesis (Ph.D.)--University of California, Los Angeles, 2021.

This item must not be sold to any third party vendors.

We define splitting surfaces in contact manifolds, and develop a technique for decomposing the strong or exact symplectic fillings of a contact manifold which admits such a surface, using Eliashberg's strategy of filling by holomorphic discs. We then apply this technique to the symplectic filling classification problem for several families of contact manifolds. In particular, we complete the classification of exact fillings for lens spaces, virtually overtwisted torus bundles, and virtually overtwisted circle bundles over Riemann surfaces. We also produce classification results for contact manifolds obtained by surgery on Legendrian negative cables, and for large families of contact structures on Seifert fibered spaces.

ISBN: 9798516079566Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Contact manifolds

Some Classification Results for Symplectic Fillings of Contact 3-Manifolds.
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008 241004s2021 ||||||||||||||||| ||eng d
020 $a 9798516079566
035 $a (MiAaPQ)AAI28544134
035 $a AAI28544134
040 $a MiAaPQ $c MiAaPQ
100 1 $a Christian, Austin. $3 3686084
245 1 0 $a Some Classification Results for Symplectic Fillings of Contact 3-Manifolds.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 143 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-01, Section: B.
500 $a Advisor: Honda, Ko.
502 $a Thesis (Ph.D.)--University of California, Los Angeles, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a We define splitting surfaces in contact manifolds, and develop a technique for decomposing the strong or exact symplectic fillings of a contact manifold which admits such a surface, using Eliashberg's strategy of filling by holomorphic discs. We then apply this technique to the symplectic filling classification problem for several families of contact manifolds. In particular, we complete the classification of exact fillings for lens spaces, virtually overtwisted torus bundles, and virtually overtwisted circle bundles over Riemann surfaces. We also produce classification results for contact manifolds obtained by surgery on Legendrian negative cables, and for large families of contact structures on Seifert fibered spaces.
590 $a School code: 0031.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Contact manifolds
653 $a Lens spaces
653 $a Torus bundles
690 $a 0405
690 $a 0642
710 2 $a University of California, Los Angeles. $b Mathematics 0540. $3 2096468
773 0 $t Dissertations Abstracts International $g 83-01B.
790 $a 0031
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28544134