Polynomial invariants of graphs on surfaces

IF 1 2区数学 Q1 MATHEMATICS

Quantum Topology Pub Date : 2010-12-22 DOI:10.4171/QT/35

R. Askanazi, S. Chmutov, C. Estill, J. Michel, P. Stollenwerk

引用次数: 15

Abstract

For a graph embedded into a surface, we relate many combinatorial parameters of the cycle matroid of the graph and the bond matroid of the dual graph with the topological parameters of the embedding. This will give an expression of the polynomial, defined by M. Las Vergnas in a combinatorial way using matroids as a specialization of the Krushkal polynomial, defined using the symplectic structure in the first homology group of the surface.

查看原文本刊更多论文

曲面上图的多项式不变量

对于嵌入曲面的图，我们将图的循环矩阵和对偶图的键阵的许多组合参数与嵌入的拓扑参数联系起来。这将给出由M. Las Vergnas以组合方式定义的多项式的表达式，该多项式使用拟阵作为Krushkal多项式的专门化，使用曲面的第一个同调群中的辛结构定义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Quantum Topology Mathematics-Geometry and Topology

CiteScore

1.80

自引率

9.10%

发文量

期刊介绍： Quantum Topology is a peer reviewed journal dedicated to publishing original research articles, short communications, and surveys in quantum topology and related areas of mathematics. Topics covered include in particular: Low-dimensional Topology Knot Theory Jones Polynomial and Khovanov Homology Topological Quantum Field Theory Quantum Groups and Hopf Algebras Mapping Class Groups and Teichmüller space Categorification Braid Groups and Braided Categories Fusion Categories Subfactors and Planar Algebras Contact and Symplectic Topology Topological Methods in Physics.