Sökning: "invariants"

Visar resultat 1 - 5 av 78 avhandlingar innehållade ordet invariants.

  1. 1. Tame representations in Topological Data Analysis: decompositions, invariants and metrics

    Författare :Francesca Tombari; Wojciech Chachólski; Patrizio Frosini; Peter Bubenik; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; topological data analysis; tameness; decompositions; invariants; metrics; Matematik; Mathematics;

    Sammanfattning : This thesis is a compilation of results that can be framed within the field of applied topology. The starting point of our study is objects presenting a possibly complex intrinsic geometry. The main goal is then to simplify, without trivializing, the geometric information characterising these objects by choosing an appropriate representation. LÄS MER

  3. 2. Arnold-type invariants of curves and wave fronts on surfaces

    Författare :Vladimir Tchernov; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Immersion of the circle; generic immersion; curves on surfaces; Legendrian immersion; Legendrian knot; wave fronts on surfaces; Whitney index; Maslov index; regular homotopy; perestroikas of plane curves and fronts; Arnold s basic invariants of plane curves and fronts; finite order invariants; Vassiliev invariants; homotopy groups of the space of curves on a surface; MATEMATIK; MATHEMATICS; MATEMATIK; matematik; Mathematics;

    Sammanfattning : This thesis is devoted to the study of invariants of generic curves and wave fronts on surfaces. The invariants J± and St were axiomatically defined by Arnold as numerical characteristics of generic curves (immersions of the circle)on ℝ2 he introduced J± in the case of generic planar wave fronts. LÄS MER

  4. 3. Invariants of knot diagrams and diagrammatic knot invariants

    Författare :Olof-Petter Östlund; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Knot theory; knot diagram; plane curve; Reidemeister move; finite degree invariant; combinatorial knot invariant; Gauss diagram; MATEMATIK; MATHEMATICS; MATEMATIK; matematik; Mathematics;

    Sammanfattning : Two knot diagrams describe isotopic knots if and only if they can be connected by a sequence of planar isotopies and Reidemeister moves (cusp-, self-tangency-, and triple point moves). In this dissertation classes of knot diagrams, Reidemeister moves, and relations between sequences of Reidemeister moves are investigated, in a manner inspired by V. LÄS MER

  5. 4. Invariants for Multidimensional Persistence

    Författare :Martina Scolamiero; Wojciech Chacholski; Vin de Silva; KTH; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; computational topology; Matematik; Mathematics;

    Sammanfattning : The amount of data that our digital society collects is unprecedented. This represents a valuable opportunity to improve our quality of life by gaining insights about complex problems related to neuroscience, medicine and biology among others. LÄS MER

  7. 5. Stable invariants of some topological moduli spaces

    Författare :Erik Lindell; Dan Petersen; Alexander Berglund; Andrew Putman; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Moduli spaces; mapping class groups; stable invariants; matematik; Mathematics;

    Sammanfattning : This thesis consists of three papers, treating stability phenomena in various automorphism groups in topology. In Papers I and III, we study the group (co)homology of certain mapping class groups of surfaces and graphs, or their respective Torelli subgroups, while the subject of Paper II is homotopy automorphisms of higher-dimensional spaces and manifolds. LÄS MER