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

Spatial graph as connected sum of a planar graph and a braid Full article

Journal

Journal of Knot Theory and its Ramifications
ISSN: 0218-2165

Output data

Year: 2021, Volume: 30, Number: 11, Article number : 2150077, Pages count : DOI: 10.1142/S0218216521500772

Tags

braid; fundamental group of spatial graph; planar graph; Spatial graph; tangle

Authors

Bardakov V.G. ^1,2,3,4 , Kawauchi A. ⁵

Affiliations

1	Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, Novosibirsk, 630090, Russian Federation
3	Novosibirsk State Agrarian University, Dobrolyubova Street, Novosibirsk, 630039, Russian Federation
4	Tomsk State University, pr. Lenina, Tomsk, 634050, Russian Federation
5	Department of Mathematics, Osaka City University Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan

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. © 2021 World Scientific Publishing Company.

Bardakov V.G. , Kawauchi A.
Spatial graph as connected sum of a planar graph and a braid
Journal of Knot Theory and its Ramifications. 2021. V.30. N11. 2150077 . DOI: 10.1142/S0218216521500772 WOS Scopus OpenAlex

Web of science:	WOS:000751830100002
Scopus:	2-s2.0-85123988870
OpenAlex:	W4205337565

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