TY - JOUR

T1 - Spatial graph as connected sum of a planar graph and a braid

AU - Bardakov, Valeriy G.

AU - Kawauchi, Akio

N1 - The authors thank Vera Gorbunova, who drew pictures for the paper. The first author is supported by the Ministry of Science and Higher Education of Russia (Agreement No. 075-02-2021-1392). Publisher Copyright: © 2021 World Scientific Publishing Company.

PY - 2021/10/1

Y1 - 2021/10/1

N2 - In this paper, we show that every finite spatial graph is a connected sum of a planar graph, which is a forest, and a tangle. As a consequence, we get that any finite spatial graph is a connected sum of a planar graph and a braid. Using these decompositions it is not difficult to find a set of generators and defining relations for the fundamental group of compliment of a spatial graph in 3-space 3.

AB - In this paper, we show that every finite spatial graph is a connected sum of a planar graph, which is a forest, and a tangle. As a consequence, we get that any finite spatial graph is a connected sum of a planar graph and a braid. Using these decompositions it is not difficult to find a set of generators and defining relations for the fundamental group of compliment of a spatial graph in 3-space 3.

KW - braid

KW - fundamental group of spatial graph

KW - planar graph

KW - Spatial graph

KW - tangle

UR - http://www.scopus.com/inward/record.url?scp=85123988870&partnerID=8YFLogxK

U2 - 10.1142/S0218216521500772

DO - 10.1142/S0218216521500772

M3 - Article

AN - SCOPUS:85123988870

VL - 30

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 11

M1 - 2150077

ER -