منابع مشابه
Combinatorial map as multiplication of combinatorial knots
We show that geometrical map can be expressed as multiplication of combinatorial maps, i.e. map P is equal to multiplication of its knot, inner knot’s square and trivial knot (= μ · ν · π1).
متن کاملRandom Knots
Introduction: A knot is a non-intersecting closed curved in 3-space. The projection of a knot onto the plane yields a knot diagram of the knot. The crossing number of a knot is the minimum number of self-crossings a knot has among all its knot diagrams. We may manipulate a given knot diagram by twisting and moving the curve so that the new diagram obtained after such manipulations is still that...
متن کاملCombinatorial Knot Contact Homology and Transverse Knots
We give a combinatorial treatment of transverse homology, a new invariant of transverse knots that is an extension of knot contact homology. The theory comes in several flavors, including one that is an invariant of topological knots and produces a three-variable knot polynomial related to the A-polynomial. We provide a number of computations of transverse homology that demonstrate its effectiv...
متن کاملLegendrian knots, transverse knotsand combinatorial Floer homology
Manolescu, Ozsváth and Sarkar gave [9] an explicit description of knot Floer homology for a knot in the three-sphere as the homology groups of a chain complex CK which is described in terms of the combinatorics of a grid diagram for a knot. In fact, the constructions of [9] are done with coefficients in Z=2Z; a lift of these constructions to coefficients in Z is given by Manolescu and the autho...
متن کاملScaling behavior of random knots.
Using numerical simulations we investigate how overall dimensions of random knots scale with their length. We demonstrate that when closed non-self-avoiding random trajectories are divided into groups consisting of individual knot types, then each such group shows the scaling exponent of approximately 0.588 that is typical for self-avoiding walks. However, when all generated knots are grouped t...
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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2020
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2020.13.633