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Symmetric Spaces and Knot Invariants...

Daemi, Aliakbar.

Symmetric Spaces and Knot Invariants from Gauge Theory.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Symmetric Spaces and Knot Invariants from Gauge Theory./
Author:	Daemi, Aliakbar.
Description:	1 online resource (98 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 75-10(E), Section: B.
Contained By:	Dissertation Abstracts International75-10B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781321015409

Symmetric Spaces and Knot Invariants from Gauge Theory.
Daemi, Aliakbar.

Symmetric Spaces and Knot Invariants from Gauge Theory. - 1 online resource (98 pages)

Source: Dissertation Abstracts International, Volume: 75-10(E), Section: B.

Thesis (Ph.D.)--Harvard University, 2014.

Includes bibliographical references

In this thesis, we set up a framework to define knot invariants for each choice of a symmetric space. In order to address this task, we start by defining appropriate notions of singular bundles and singular connections for a given symmetric space. We can associate a moduli space to any singular bundle defined over a compact 4-manifold with possibly non-empty boundary. We study these moduli spaces and show that they enjoy nice properties. For example, in the case of the symmetric space SU(n)/ SO(n) the moduli space can be perturbed to an orientable manifold. Although this manifold is not necessarily compact, we introduce a comapctification of it. We then use this moduli space for singular bundles defined over 4-manifolds of the form Y x R to define knot invariants. In another direction we mimic the construction of Donaldson invariants to define polynomial invariants for closed 4-manifolds equipped with smooth action of Z/2Z.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781321015409Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Symmetric Spaces and Knot Invariants from Gauge Theory.
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020 $a 9781321015409
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035 $a (MiAaPQ)gsas.harvard:11563
035 $a AAI3626542
040 $a MiAaPQ $b eng $c MiAaPQ $d NTU
100 1 $a Daemi, Aliakbar. $3 1193135
245 1 0 $a Symmetric Spaces and Knot Invariants from Gauge Theory.
264 0 $c 2014
300 $a 1 online resource (98 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 75-10(E), Section: B.
500 $a Adviser: Peter B. Kronheimer.
502 $a Thesis (Ph.D.)--Harvard University, 2014.
504 $a Includes bibliographical references
520 $a In this thesis, we set up a framework to define knot invariants for each choice of a symmetric space. In order to address this task, we start by defining appropriate notions of singular bundles and singular connections for a given symmetric space. We can associate a moduli space to any singular bundle defined over a compact 4-manifold with possibly non-empty boundary. We study these moduli spaces and show that they enjoy nice properties. For example, in the case of the symmetric space SU(n)/ SO(n) the moduli space can be perturbed to an orientable manifold. Although this manifold is not necessarily compact, we introduce a comapctification of it. We then use this moduli space for singular bundles defined over 4-manifolds of the form Y x R to define knot invariants. In another direction we mimic the construction of Donaldson invariants to define polynomial invariants for closed 4-manifolds equipped with smooth action of Z/2Z.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Harvard University. $b Mathematics. $3 1193029
773 0 $t Dissertation Abstracts International $g 75-10B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3626542 $z click for full text (PQDT)

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