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Collapsibility and Z-Compactifications of Cat(0) Cube Complexes.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Collapsibility and Z-Compactifications of Cat(0) Cube Complexes./
Author:	Gulbrandsen, Daniel L.
Description:	1 online resource (96 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-03, Section: B.
Contained By:	Dissertations Abstracts International85-03B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798380163330

Collapsibility and Z-Compactifications of Cat(0) Cube Complexes.
Gulbrandsen, Daniel L.

Collapsibility and Z-Compactifications of Cat(0) Cube Complexes. - 1 online resource (96 pages)

Source: Dissertations Abstracts International, Volume: 85-03, Section: B.

Thesis (Ph.D.)--The University of Wisconsin - Milwaukee, 2023.

Includes bibliographical references

We extend the notion of collapsibility to non-compact complexes and prove collapsibility of locally-finite CAT(0) cube complexes. Namely, we construct such a cube complex X out of nested convex compact subcomplexes {Ci} ∞i=0 with the properties that X = ∪ ∞i=0Ci and Ci collapses to Ci−1 for all i ≥ 1.We then define bonding maps ri between the compacta Ci and construct an inverse sequence yielding the inverse limit space lim←−{Ci , ri}. This will provide a new way of Z-compactifying X. In particular, the process will yield a new Z-boundary, called the cubical boundary.

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

Mode of access: World Wide Web

ISBN: 9798380163330Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

BoundariesIndex Terms--Genre/Form:

554714
Electronic books.

Collapsibility and Z-Compactifications of Cat(0) Cube Complexes.
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100 1 $a Gulbrandsen, Daniel L. $3 1474106
245 1 0 $a Collapsibility and Z-Compactifications of Cat(0) Cube Complexes.
264 0 $c 2023
300 $a 1 online resource (96 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 85-03, Section: B.
500 $a Advisor: Guilbault, Craig R.
502 $a Thesis (Ph.D.)--The University of Wisconsin - Milwaukee, 2023.
504 $a Includes bibliographical references
520 $a We extend the notion of collapsibility to non-compact complexes and prove collapsibility of locally-finite CAT(0) cube complexes. Namely, we construct such a cube complex X out of nested convex compact subcomplexes {Ci} ∞i=0 with the properties that X = ∪ ∞i=0Ci and Ci collapses to Ci−1 for all i ≥ 1.We then define bonding maps ri between the compacta Ci and construct an inverse sequence yielding the inverse limit space lim←−{Ci , ri}. This will provide a new way of Z-compactifying X. In particular, the process will yield a new Z-boundary, called the cubical boundary.
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 Applied mathematics. $3 1069907
653 $a Boundaries
653 $a Collapsibility
653 $a Topology
653 $a Z-sets
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a The University of Wisconsin - Milwaukee. $b Mathematics. $3 1188708
773 0 $t Dissertations Abstracts International $g 85-03B.
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