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New Examples of Collapse with Lower Curvature Bound.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	New Examples of Collapse with Lower Curvature Bound./
Author:	Benavides, Jesse.
Description:	1 online resource (96 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
Contained By:	Dissertation Abstracts International78-10B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369833256

New Examples of Collapse with Lower Curvature Bound.
Benavides, Jesse.

New Examples of Collapse with Lower Curvature Bound. - 1 online resource (96 pages)

Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

In this work, we describe a method to construct new eXamples of collapse with a lower curvature bound inspired by Cheeger and Gromov. Unlike with collapse with an upper and lower curvature bound, which is now completely understood, the structure of collapse with a lower curvature bound is still a mystery.

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

Mode of access: World Wide Web

ISBN: 9781369833256Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

New Examples of Collapse with Lower Curvature Bound.
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100 1 $a Benavides, Jesse. $3 1180614
245 1 0 $a New Examples of Collapse with Lower Curvature Bound.
264 0 $c 2017
300 $a 1 online resource (96 pages)
336 $a text $b txt $2 rdacontent
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500 $a Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
500 $a Adviser: Frederick Wilhelm.
502 $a Thesis (Ph.D.) $c University of California, Riverside $d 2017.
504 $a Includes bibliographical references
520 $a In this work, we describe a method to construct new eXamples of collapse with a lower curvature bound inspired by Cheeger and Gromov. Unlike with collapse with an upper and lower curvature bound, which is now completely understood, the structure of collapse with a lower curvature bound is still a mystery.
520 $a In [5], Grove and Petersen showed that if a sequence of Riemannian manifolds (Mi, gi) has uniform lower curvature bound, k, and Mi → X, then X is an AleXandrov space with lower curvature bound k. Petersen, Wilhelm, and Zhu then showed that the converse is false [9]. Perelman showed that given a sequence of n-dimensional Alexandrov spaces with a uniform lower curvature bound, with limit space X such that dim X = n, all but finitely many of the prelimits are homeomorphic to X.
520 $a In 1985, Cheeger and Gromov introduced the concept of an F-structure, which can be thought as a generalized torus action on a manifold [1]. They showed that a manifold collapses with bounded curvature if and only if it admits an F-structure [2]. An F-structure is an example of a more general construct known as a g-structure, which is a sheaf of Lie groups actions, and is one of the main tools used in our approach.
520 $a The second main tool we use was also defined by Cheeger and is known as a Cheeger deformation. Cheeger generalized the method used by Berger in his classic example now known as the Berger spheres, which helped create the study of collapse in Riemannian geometry. Berger showed that scaling the metric of S3 along the Hopf circles collapses S3 to the 2-sphere of radius 12.
520 $a In this work, using g-structures and Cheeger deformations, we construct new examples of collapse with a lower curvature bound.
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 University of California, Riverside. $b Mathematics. $3 1180615
773 0 $t Dissertation Abstracts International $g 78-10B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10258678 $z click for full text (PQDT)