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Monopoles and Dehn Twists on Contact 3-Manifolds.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Monopoles and Dehn Twists on Contact 3-Manifolds./
Author:	Echaniz, Juan Alvaro Munoz .
Description:	1 online resource (178 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-10, Section: A.
Contained By:	Dissertations Abstracts International84-10A.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30419649click for full text (PQDT)
ISBN:	9798379422240

Monopoles and Dehn Twists on Contact 3-Manifolds.
Echaniz, Juan Alvaro Munoz .

Monopoles and Dehn Twists on Contact 3-Manifolds. - 1 online resource (178 pages)

Source: Dissertations Abstracts International, Volume: 84-10, Section: A.

Thesis (Ph.D.)--Columbia University, 2023.

Includes bibliographical references

In this dissertation, we study the isotopy problem for a certain three-dimensional contactomorphism which is supported in a neighbourhood of an embedded 2-sphere with standard characteristic foliation. The diffeomorphism which underlies it is the Dehn twist on the sphere, and therefore its square becomes smoothly isotopic to the identity. The main result of this dissertation gives conditions under which any iterate of the Dehn twist along a non-trivial sphere is not contact isotopic to the identity. This provides the first examples of exotic contactomorphisms with infinite order in the contact mapping class group, as well as the first examples of exotic contactomorphisms of 3-manifolds with b1 = 0. The proof crucially relies on the construction of an invariant for families of contact structures in monopole Floer homology which generalises the Kronheimer-Mrowka-Ozsvath-Szabo contact invariant, together with the nice interaction between this families invariant and the \uD835\uDC48 map in Floer homology. This is based on material that appeared in.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798379422240Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

3-dimensional contact topologyIndex Terms--Genre/Form:

542853
Electronic books.

Monopoles and Dehn Twists on Contact 3-Manifolds.
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100 1 $a Echaniz, Juan Alvaro Munoz . $3 3699132
245 1 0 $a Monopoles and Dehn Twists on Contact 3-Manifolds.
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300 $a 1 online resource (178 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 84-10, Section: A.
500 $a Advisor: Lin, Francesco.
502 $a Thesis (Ph.D.)--Columbia University, 2023.
504 $a Includes bibliographical references
520 $a In this dissertation, we study the isotopy problem for a certain three-dimensional contactomorphism which is supported in a neighbourhood of an embedded 2-sphere with standard characteristic foliation. The diffeomorphism which underlies it is the Dehn twist on the sphere, and therefore its square becomes smoothly isotopic to the identity. The main result of this dissertation gives conditions under which any iterate of the Dehn twist along a non-trivial sphere is not contact isotopic to the identity. This provides the first examples of exotic contactomorphisms with infinite order in the contact mapping class group, as well as the first examples of exotic contactomorphisms of 3-manifolds with b1 = 0. The proof crucially relies on the construction of an invariant for families of contact structures in monopole Floer homology which generalises the Kronheimer-Mrowka-Ozsvath-Szabo contact invariant, together with the nice interaction between this families invariant and the \uD835\uDC48 map in Floer homology. This is based on material that appeared in.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Mathematics education. $3 641129
653 $a 3-dimensional contact topology
653 $a Gauge theory
653 $a Low dimensional topology
653 $a Monopole floer homology
653 $a Dehn twist
655 7 $a Electronic books. $2 lcsh $3 542853
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690 $a 0280
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710 2 $a Columbia University. $b Mathematics. $3 1684292
773 0 $t Dissertations Abstracts International $g 84-10A.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30419649 $z click for full text (PQDT)