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Seiberg-Witten Floer K-Theory and Cyclic Group Actions.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Seiberg-Witten Floer K-Theory and Cyclic Group Actions./
Author:	Montague, Ian.
Description:	1 online resource (304 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
Contained By:	Dissertations Abstracts International84-11B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30423925click for full text (PQDT)
ISBN:	9798379558260

Seiberg-Witten Floer K-Theory and Cyclic Group Actions.
Montague, Ian.

Seiberg-Witten Floer K-Theory and Cyclic Group Actions. - 1 online resource (304 pages)

Source: Dissertations Abstracts International, Volume: 84-11, Section: B.

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

Includes bibliographical references

Given a spin rational homology sphere Y equipped with a Z/m-action preserving the spin structure, we use the Seiberg-Witten equations to define equivariant refinements of the invariant κ(Y) from [Man14], which take the form of a finite subset of elements in a lattice constructed from the representation ring of a twisted product of Pin(2) and Z/m. The main theorems consist of equivariant relative 10/8-ths type inequalities for spin equivariant cobordisms between rational homology spheres. We provide applications to knot concordance, give obstructions to extending cyclic group actions over spin fillings, and via taking branched covers we obtain genus bounds for knots in punctured 4-manifolds. In some cases, these bounds are strong enough to determine the relative genus for a large class of knots within certain homology classes in CP 2#CP 2, S 2xS 2#S 2xS 2, CP 2#S 2xS 2, and homotopy K3 surfaces.

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

Mode of access: World Wide Web

ISBN: 9798379558260Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Rational homology sphereIndex Terms--Genre/Form:

542853
Electronic books.

Seiberg-Witten Floer K-Theory and Cyclic Group Actions.
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245 1 0 $a Seiberg-Witten Floer K-Theory and Cyclic Group Actions.
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300 $a 1 online resource (304 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
500 $a Advisor: Ruberman, Daniel.
502 $a Thesis (Ph.D.)--Brandeis University, 2023.
504 $a Includes bibliographical references
520 $a Given a spin rational homology sphere Y equipped with a Z/m-action preserving the spin structure, we use the Seiberg-Witten equations to define equivariant refinements of the invariant κ(Y) from [Man14], which take the form of a finite subset of elements in a lattice constructed from the representation ring of a twisted product of Pin(2) and Z/m. The main theorems consist of equivariant relative 10/8-ths type inequalities for spin equivariant cobordisms between rational homology spheres. We provide applications to knot concordance, give obstructions to extending cyclic group actions over spin fillings, and via taking branched covers we obtain genus bounds for knots in punctured 4-manifolds. In some cases, these bounds are strong enough to determine the relative genus for a large class of knots within certain homology classes in CP 2#CP 2, S 2xS 2#S 2xS 2, CP 2#S 2xS 2, and homotopy K3 surfaces.
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 Theoretical mathematics. $3 3173530
653 $a Rational homology sphere
653 $a Spin structure
653 $a Equivariant relative
653 $a Spin fillings
655 7 $a Electronic books. $2 lcsh $3 542853
690 $a 0405
690 $a 0642
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710 2 $a Brandeis University. $b Mathematics. $3 1285724
773 0 $t Dissertations Abstracts International $g 84-11B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30423925 $z click for full text (PQDT)