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C*-Algebraic Higher Signatures on No...

Liu, Mingyu.

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

Record Type:	Electronic resources : Monograph/item
Title/Author:	C*-Algebraic Higher Signatures on Non-Witt Spaces./
Author:	Liu, Mingyu.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	95 p.
Notes:	Source: Dissertations Abstracts International, Volume: 83-11, Section: B.
Contained By:	Dissertations Abstracts International83-11B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29241632
ISBN:	9798438744672

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

C*-Algebraic Higher Signatures on Non-Witt Spaces. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 95 p.

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

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

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.

ISBN: 9798438744672Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Signature

C*-Algebraic Higher Signatures on Non-Witt Spaces.
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300 $a 95 p.
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.
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.
590 $a School code: 0803.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Signature
653 $a Non-Witt space
653 $a Geometry
653 $a Topology
653 $a Noncommutative geometric methods
690 $a 0405
690 $a 0642
710 2 $a Texas A&M University. $b Mathematics. $3 3769861
773 0 $t Dissertations Abstracts International $g 83-11B.
790 $a 0803
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29241632