On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups

On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups

Bibliographic Details
Main Author: Kim, Raeyong
Language:English
Published: The Ohio State University / OhioLINK 2012
Subjects:
Mathematics
CAT(0) groups
Kan-Thurston theorem
algebraic rank
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=osu1343805338
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-osu13438053382021-08-03T06:06:17Z On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups Kim, Raeyong Mathematics CAT(0) groups Kan-Thurston theorem algebraic rank This thesis is divided into two parts.In chapter 2, we study two generalizations of the Kan-Thurston theorem. The Kan-Thuston theorem says that every complex X has the homology of some group G. As a combination of Hausmann and Leary, we prove that G can be taken as a CAT(0) cubical group if X is finite. We also prove that every finite complex is homotopy equivalent to the classifying space for proper bundles of a virtual Poincar ¿¿¿¿e duality group. Coxeter groups will be introduced to construct the virtual Poincar ¿¿¿¿e duality group.In chapter 3, we study algebraic rank of groups. It is specially interesting when groups act properly and cocompactly on CAT(0) spaces by isometries. Motivated by the strong relationship between geometric rank of CAT(0) manifolds and alge- braic rank of CAT(0) groups, we compute algebraic rank of some CAT(0) groups. They include right-angled Coxeter groups, right-angled Artin groups, groups acting geometrically on CAT(0) spaces with isolated flats and relatively hyperbolic groups. 2012-08-28 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1343805338 http://rave.ohiolink.edu/etdc/view?acc_num=osu1343805338 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Mathematics
CAT(0) groups
Kan-Thurston theorem
algebraic rank
spellingShingle Mathematics
CAT(0) groups
Kan-Thurston theorem
algebraic rank
Kim, Raeyong
On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups
author Kim, Raeyong
author_facet Kim, Raeyong
author_sort Kim, Raeyong
title On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups
title_short On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups
title_full On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups
title_fullStr On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups
title_full_unstemmed On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups
title_sort on the theorem of kan-thurston and algebraic rank of cat(0) groups
publisher The Ohio State University / OhioLINK
publishDate 2012
url http://rave.ohiolink.edu/etdc/view?acc_num=osu1343805338
work_keys_str_mv AT kimraeyong onthetheoremofkanthurstonandalgebraicrankofcat0groups
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