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Automorphisms of Nonpositively Curve...

ProQuest Information and Learning Co.

Automorphisms of Nonpositively Curved Cube Complexes, Right-Angled Artin Groups and Homology.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Automorphisms of Nonpositively Curved Cube Complexes, Right-Angled Artin Groups and Homology./
Author:	Bregman, Corey.
Description:	1 online resource (86 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.
Contained By:	Dissertation Abstracts International79-04B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355370614

Automorphisms of Nonpositively Curved Cube Complexes, Right-Angled Artin Groups and Homology.
Bregman, Corey.

Automorphisms of Nonpositively Curved Cube Complexes, Right-Angled Artin Groups and Homology. - 1 online resource (86 pages)

Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

Recently, the geometry of CAT(0) cube complexes featured prominently in Agol's resolution of two longstanding conjectures of Thurston in low-dimensional topology: the virtually Haken and virtually fibered conjecture for hyperbolic 3-manifolds. A key step of the proof was to show that every hyperbolic 3-manifold group is virtually special, i.e. virtually the fundamental group of a special nonpositively curved (NPC) cube complex. In this thesis, we study algebraic properties of special groups as they relate to the geometry of special cube complexes.

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

Mode of access: World Wide Web

ISBN: 9780355370614Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Automorphisms of Nonpositively Curved Cube Complexes, Right-Angled Artin Groups and Homology.
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035 $a (MiAaPQ)0187rice:2123Bregman
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040 $a MiAaPQ $b eng $c MiAaPQ
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100 1 $a Bregman, Corey. $3 1180986
245 1 0 $a Automorphisms of Nonpositively Curved Cube Complexes, Right-Angled Artin Groups and Homology.
264 0 $c 2017
300 $a 1 online resource (86 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: 79-04(E), Section: B.
500 $a Advisers: Andrew Putman; Michael Wolf.
502 $a Thesis (Ph.D.) $c Rice University $d 2017.
504 $a Includes bibliographical references
520 $a Recently, the geometry of CAT(0) cube complexes featured prominently in Agol's resolution of two longstanding conjectures of Thurston in low-dimensional topology: the virtually Haken and virtually fibered conjecture for hyperbolic 3-manifolds. A key step of the proof was to show that every hyperbolic 3-manifold group is virtually special, i.e. virtually the fundamental group of a special nonpositively curved (NPC) cube complex. In this thesis, we study algebraic properties of special groups as they relate to the geometry of special cube complexes.
520 $a In the first part of the thesis, we introduce a positive integer-valued invariant of special cube complexes called the genus, and show that having genus one is equivalent to having free abelian fundamental group. As a corollary, we obtain a new proof of the fact that every special group is either abelian or surjects onto a non-abelian free group. In the second part of the thesis, we turn our attention to automorphisms of NPC cube complexes. We give a criterion on a special cube complex which implies that any automorphism acts non-trivially on first homology, and show that a non- trivial action on homology can always be achieved by passing to covers. We then apply the criterion to provide a new geometric proof that the Torelli subgroup for a right-angled Artin group is torsion-free.
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 Rice University. $b Mathematics. $3 1180985
773 0 $t Dissertation Abstracts International $g 79-04B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10670662 $z click for full text (PQDT)

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