Browsing by Author "Alexander Olshanskiy"

Now showing items 1-7 of 7

    • Cohomology of group theoretic Dehn fillings 
      Sun, Bin (2019-05-24)
      Department: Mathematics
      This thesis aims to study cohomology of group theoretic Dehn fillings. For sufficiently deep Dehn fillings of hyperbically embedded subgroups, we first prove that Dehn filling kernels enjoy a particular free product ...
    • On geometry and combinatorics of van Kampen diagrams 
      Muranov, Alexey (2006-06-05)
      Department: Mathematics
      The subject of this work is application of combinatorial group theory to the problem of constructing groups with prescribed properties. It is shown how certain groups can be presented by generators and defining relations, thus ...
    • On Quasiconvex Subsets of Hyperbolic Groups 
      Minasyan, Ashot (2005-06-29)
      Department: Mathematics
      A geodesic metric space $X$ is called hyperbolic if there exists $delta ge 0$ such that every geodesic triangle $Delta$ in $X$ is $delta$-slim, i.e., each side of $Delta$ is contained in a closed $delta$-neighborhood of ...
    • Partial-Burnside Groups 
      Boatman, Nicholas Stephen (2012-11-30)
      Department: Mathematics
      We consider groups which have a presentation whose defining relators are all nth powers and in which every element has order dividing n, for a fixed odd n that is sufficiently large. Such groups are called Partial-Burnside ...
    • Percolation and Ising Model on Graphs with Tree-like Structure 
      Kozakova, Iva (2008-12-11)
      Department: Mathematics
      In the main part of this dissertation we present a method for finding the critical probability for the Bernoulli bond percolation and the critical inverse temperature for Ising model on graphs with the so-called tree-like ...
    • Properties of acylindrically hyperbolic groups and their small cancellation quotients 
      Hull, Michael Bradley (2013-04-16)
      Department: Mathematics
      We investigate the class of acylindrically hyperbolic groups, which includes many examples of groups which admit natural actions on hyperbolic metric spaces, such as hyperbolic and relatively hyperbolic groups, mapping ...
    • Properties of hyperbolic groups: free normal subgroups, quasiconvex subgroups and actions of maximal growth 
      Chaynikov, Vladimir Vladimirovich (2012-06-22)
      Department: Mathematics
      Hyperbolic groups are defined using the analogy between algebraic objects – groups – and hyperbolic metric spaces and manifolds. Our research involves the study and use of two very different, yet very natural, classes of ...