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C*-Algebraic Higher Signatures on Non-Witt Spaces.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	C*-Algebraic Higher Signatures on Non-Witt Spaces./
Author:	Liu, Mingyu.
Description:	1 online resource (95 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 83-11, Section: B.
Contained By:	Dissertations Abstracts International83-11B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798438744672

C*-Algebraic Higher Signatures on Non-Witt Spaces.
Liu, Mingyu.

C*-Algebraic Higher Signatures on Non-Witt Spaces. - 1 online resource (95 pages)

Source: Dissertations Abstracts International, Volume: 83-11, Section: B.

Thesis (Ph.D.)--Texas A&M University, 2021.

Includes bibliographical references

Signature plays an important role in geometry and topology. In the space with singularity, Goresky and MacPherson extend the signatures to oriented pseudomanifolds with only even codimensional stratums by using generalized Poincare duality of intersection homology. After that Siegel extended the signature on Witt spaces. Higson and Xie study the C∗-higher signature on Witt space. Non-Witt spaces need a refined intersection homology to hold Poincare duality. Followed by the combinatorial framework developed by Higson and Roe, this dissertation construct the C∗-signature on non Witt space with noncommutative geometric methods. In conical singular case, we compare analytical signature of smooth stratified non Witt space by Albin, Leichtnam, Mazzeo and Piazza.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798438744672Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

SignatureIndex Terms--Genre/Form:

554714
Electronic books.

C*-Algebraic Higher Signatures on Non-Witt Spaces.
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500 $a Source: Dissertations Abstracts International, Volume: 83-11, Section: B.
500 $a Advisor: Xie, Zhizhang.
502 $a Thesis (Ph.D.)--Texas A&M University, 2021.
504 $a Includes bibliographical references
520 $a Signature plays an important role in geometry and topology. In the space with singularity, Goresky and MacPherson extend the signatures to oriented pseudomanifolds with only even codimensional stratums by using generalized Poincare duality of intersection homology. After that Siegel extended the signature on Witt spaces. Higson and Xie study the C∗-higher signature on Witt space. Non-Witt spaces need a refined intersection homology to hold Poincare duality. Followed by the combinatorial framework developed by Higson and Roe, this dissertation construct the C∗-signature on non Witt space with noncommutative geometric methods. In conical singular case, we compare analytical signature of smooth stratified non Witt space by Albin, Leichtnam, Mazzeo and Piazza.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Theoretical mathematics. $3 1180455
653 $a Signature
653 $a Non-Witt space
653 $a Geometry
653 $a Topology
653 $a Noncommutative geometric methods
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690 $a 0405
690 $a 0642
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Texas A&M University. $b Mathematics. $3 1474047
773 0 $t Dissertations Abstracts International $g 83-11B.
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