Browsing Mathematics Theses and Dissertations by Author "Dugger, Daniel"

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  • A Structure Theorem for RO(C2)-graded Cohomology 
    May, Clover (University of Oregon, 2018-09-06)
    Let C2 be the cyclic group of order two. We present a structure theorem for the RO(C2)-graded Bredon cohomology of C2-spaces using coefficients in the constant Mackey functor F2. We show that, as a module over the cohomology ...
  • Algebraic Weak Factorization Systems in Double Categories 
    Schultz, Patrick (University of Oregon, 2014-09-29)
    We present a generalized framework for the theory of algebraic weak factorization systems, building on work by Richard Garner and Emily Riehl. We define cyclic 2-fold double categories, and bimonads (or bialgebras) and ...
  • Homological Algebra for Polynomial Mackey Rings over Prime Cyclic Groups 
    Casebolt, Ross (University of Oregon, 2022-10-26)
    Let $C_l$ denote the cyclic group of prime order $l$ and let $k$ be a field. We define a Mackey $\underline{k}$-algebra $\underline{k}[x_\theta]$ which is constructed by adjoining a free commutative variable to the free ...
  • Mackey Functors over the Group Z/2 and Computations in Homological Algebra 
    Raies, Daniel (University of Oregon, 2019-09-18)
    Mackey functors over the group Z/2 are useful in the study of Z/2-equivariant cohomology. In this dissertation we establish results which are useful for homological algebra computations for certain Mackey rings over Z/2. ...
  • New A-infinity Diagonals from Contractions of the Weighted Associahedra 
    Phillips, Bo (University of Oregon, 2024-01-09)
    In this paper, we build on the work of Lipshitz, Ozsv\'{a}th, and Thurston by constructing an algorithm that generates a weighted $A_\infty$-diagonal given a family of contractions of the weighted associahedron complexes. ...
  • RO(C2)-graded Cohomology of Equivariant Grassmannian Manifolds 
    Hogle, Eric (University of Oregon, 2018-09-06)
    We compute the RO(C2)-graded Bredon cohomology of certain families of real and complex C2-equivariant Grassmannians.
  • $RO(C_3)$-graded Bredon Cohomology and $C_p$-surfaces 
    Pohland, Kelly (University of Oregon, 2022-10-04)
    Let $p$ be an odd prime, and let $C_p$ denote the cyclic group of order $p$. We use equivariant surgery methods to classify all closed, connected $2$-manifolds with an action of $C_p$. We then use this classification in ...
  • The Canonical Grothendieck Topology and a Homotopical Analog 
    Lester, Cynthia (University of Oregon, 2019-09-18)
    We explore the canonical Grothendieck topology and a new homotopical analog. First we discuss a specific description of the covers in the canonical topology, which we then use to get a corollary of Giraud's Theorem. Second ...
  • The RO(C2)-graded Cohomology of C2-Surfaces and Equivariant Fundamental Classes 
    Hazel, Christy (University of Oregon, 2020-09-24)
    Let C2 denote the cyclic group of order two. Given a manifold with a C2-action, we can consider its equivariant Bredon RO(C2)-graded cohomology. We first use a classification due to Dugger to compute the Bredon cohomology ...

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