2016/09/21 by Andrey Grinblat, Grinblat, Andrey, Viktor Lopatkin +1
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT
paper · pdf · doi:10.48550/arxiv.1610.01440
arXiv admin note: text overlap with arXiv:math/9810073, arXiv:math/0404490 by other authors
arxiv created 2017/09/04 · arxiv updated 2017/09/05
The problem of which Gauss diagram can be realized by knots is an old one and has been solved in several ways. In this paper, we present a direct approach to this problem. We show that the needed conditions for realizability of a Gauss diagram can be interpreted as follows "the number of exits = the number of entrances" and the sufficient condition is based on Jordan curve Theorem.