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

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.

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Kim, Raeyong. "On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups." Electronic Thesis or Dissertation. Ohio State University, 2012. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Kim, Raeyong "On the Theorem of Kan-Thurston and Algebraic Rank of CAT(0) groups." Electronic Thesis or Dissertation. Ohio State University, 2012. https://etd.ohiolink.edu/

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