Browsing University of Galway Theses by Author "Ellis, Graham"

Now showing items 1-6 of 6

    • Computation of cohomology operations for finite groups 

      Al-Baydli, Daher (NUI Galway, 2018-08-31)
      The main result of this dissertation is the computation of all Steenrod squares on the Mod 2 cohomology of all groups of order dividing 32 and all but 58 groups of order 64; partial information on Steenrod square is ...

    • Computational Homology of Cubical and Permutahedral Complexes 

      Hegarty, Fintan (2012-09-28)
      Homology is the study of connectivity and "holes" in spaces. The aim of this thesis is to introduce and develop a theory of permutahedral complexes for computations of homology of large data sets and to compare, using ...

    • Computational homology of n-types 

      Le, Van Luyen (2014-01-10)
      An n-type X is a CW-space with homotopy groups \pi_iX=0 for all i>n. Up to homotopy equivalence such a space can be specified algebraically by means of a simplicial group whose Moore complex is trivial in degrees >= n. For ...

    • Computing invariants of knotted manifolds 

      Killeen, Kelvin (NUI Galway, 2022-09-13)
      In this thesis, we develop algorithms in computational topology for working with regular CW-complexes and calculating associated homological invariants. We adapt the classical notion of broken surface diagrams for describing ...

    • Discrete vector fields and the cohomology of certain arithmetic and crystallographic groups 

      Bui, Anh Tuan (2015-05-26)
      This thesis has two main topics: Arithmetic groups and Crystallographic groups. The work on arithmetic groups SL(2, Z[1/m]) was motivated by a question of Kevin Hutchinson and also a generalization of the paper "On the ...

    • Groupoids and computational topology 

      Alokbi, Nisreen (NUI Galway, 2019-09-09)
      This thesis contributes to the computational theory of finitely presented groupoids. It develops, implements and illustrates data types and algorithms aimed at pure and applied topology. In particular, the thesis designs ...