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Involutive Heegaard Floer Homology a...

Dai, Irving.

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Involutive Heegaard Floer Homology and Homology Cobordism.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Involutive Heegaard Floer Homology and Homology Cobordism./
Author:	Dai, Irving.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	112 p.
Notes:	Source: Dissertations Abstracts International, Volume: 80-12, Section: B.
Contained By:	Dissertations Abstracts International80-12B.
Subject:	Theoretical Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13882762
ISBN:	9781392269756

Involutive Heegaard Floer Homology and Homology Cobordism.
Dai, Irving.

Involutive Heegaard Floer Homology and Homology Cobordism. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 112 p.

Source: Dissertations Abstracts International, Volume: 80-12, Section: B.

Thesis (Ph.D.)--Princeton University, 2019.

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

In this thesis, we present several results regarding the application of Heegaard Floer theory to the homology cobordism group. The majority of our work is concerned with giving a structural understanding of the involutive Heegaard Floer homology for linear combinations of Seifert fibered spaces. As an application, we show that if Y is a linear combination of Seifert fibered homology spheres with μ(Y) = 1, then Y is not torsion in the homology cobordism group. We also discuss what can be said about the Pin(2)-equivariant monopole Floer homology of Seifert fibered spaces using our techniques. These results give a possible approach towards showing that Seifert fibered spaces do not generate the homology cobordism group.

ISBN: 9781392269756Subjects--Topical Terms:

1672766
Theoretical Mathematics.

Involutive Heegaard Floer Homology and Homology Cobordism.
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100 1 $a Dai, Irving. $3 3437964
245 1 0 $a Involutive Heegaard Floer Homology and Homology Cobordism.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 112 p.
500 $a Source: Dissertations Abstracts International, Volume: 80-12, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Szabo, Zoltan.
502 $a Thesis (Ph.D.)--Princeton University, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a In this thesis, we present several results regarding the application of Heegaard Floer theory to the homology cobordism group. The majority of our work is concerned with giving a structural understanding of the involutive Heegaard Floer homology for linear combinations of Seifert fibered spaces. As an application, we show that if Y is a linear combination of Seifert fibered homology spheres with μ(Y) = 1, then Y is not torsion in the homology cobordism group. We also discuss what can be said about the Pin(2)-equivariant monopole Floer homology of Seifert fibered spaces using our techniques. These results give a possible approach towards showing that Seifert fibered spaces do not generate the homology cobordism group.
590 $a School code: 0181.
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773 0 $t Dissertations Abstracts International $g 80-12B.
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793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13882762