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

Kim, Raeyong
http://rave.ohiolink.edu/etdc/view?acc_num=osu1343805338

Abstract Details

2012, Doctor of Philosophy, Ohio State University, Mathematics.
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.
Jean Lafont (Advisor)
Ian Leary (Advisor)
Michael Davis (Committee Member)
Nathan Broaddus (Committee Member)
57 p.
Mathematics
CAT(0) groups; Kan-Thurston theorem; algebraic rank

Recommended Citations

Citations

  • Kim, R. (2012). On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1343805338

    APA Style (7th edition)

  • Kim, Raeyong. On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups. 2012. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1343805338.

    MLA Style (8th edition)

  • Kim, Raeyong. "On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups." Doctoral dissertation, Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1343805338

    Chicago Manual of Style (17th edition)

osu1343805338
769
© 2012, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.