Sökning: "Vassiliev invariants"

Hittade 2 avhandlingar innehållade orden Vassiliev invariants.

1. 1. 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

3. 2. 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