Sökning: "homotopy theory"

Visar resultat 1 - 5 av 37 avhandlingar innehållade orden homotopy theory.

  1. 1. Homotopy Theory and TDA with a View Towards Category Theory

    Författare :Sebastian Öberg; Wojciech Chachólski; David Blanc; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Homotopy theory; Topological Data Analysis; Category theory; Mapping spaces; Homotopy commutative diagrams; Matematik; Mathematics;

    Sammanfattning : This thesis contains three papers. Paper A and Paper B deal with homotopy theory and Paper C deals with Topological Data Analysis. All three papers are written from a categorical point of view.In Paper A we construct categories of short hammocks and show that their weak homotopy type is that of mapping spaces. LÄS MER

  3. 2. Formality and homotopy automorphisms in rational homotopy theory

    Författare :Bashar Saleh; Alexander Berglund; Marco Manetti; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Rational homotopy theory; formality; homotopy automorphisms; Mathematics; matematik;

    Sammanfattning : This licentiate thesis consists of two papers treating subjects in rational homotopy theory.In Paper I, we establish two formality conditions in characteristic zero. We prove that adg Lie algebra is formal if and only if its universal enveloping algebra is formal. LÄS MER

  4. 3. Formality and rational homotopy theory of relative homotopy automorphisms

    Författare :Bashar Saleh; Alexander Berglund; Aniceto Murillo; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; rational homotopy theory; formality; relative homotopy automorphisms; Mathematics; matematik;

    Sammanfattning : This PhD thesis consists of four papers treating topics in rational homotopy theory.In Paper I, we establish two formality conditions in characteristic zero. We prove that a dg Lie algebra is formal if and only if its universal enveloping algebra is formal. LÄS MER

  5. 4. Hopf Invariants in Real and Rational Homotopy Theory

    Författare :Felix Wierstra; Alexander Berglund; Urtzi Buijs; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Rational homotopy theory; Real homotopy theory; operads; Hopf invariants; Mathematics; matematik;

    Sammanfattning : In this thesis we use the theory of algebraic operads to define a complete invariant of real and rational homotopy classes of maps of topological spaces and manifolds. More precisely let f,g : M -> N be two smooth maps between manifolds M and N. LÄS MER

  7. 5. Univalent Types, Sets and Multisets : Investigations in dependent type theory

    Författare :Håkon Robbestad Gylterud; Erik Palmgren; Nicola Gambino; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; type theory; homotopy type theory; dependent types; constructive set theory; databases; formalisation; agda; Mathematics; matematik;

    Sammanfattning : This thesis consists of four papers on type theory and a formalisation of certain results from the two first papers in the Agda language. We cover topics such as models of multisets and sets in Homotopy Type Theory, and explore ideas of using type theory as a language for databases and different ways of expressing dependencies between terms. LÄS MER