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Spatial graph as connected sum of a planar graph and a braid. / Bardakov, Valeriy G.; Kawauchi, Akio.

In: Journal of Knot Theory and its Ramifications, Vol. 30, No. 11, 2150077, 01.10.2021.

Research output: Contribution to journal › Article › peer-review

Harvard

Bardakov, VG & Kawauchi, A 2021, 'Spatial graph as connected sum of a planar graph and a braid', Journal of Knot Theory and its Ramifications, vol. 30, no. 11, 2150077. https://doi.org/10.1142/S0218216521500772

APA

Bardakov, V. G., & Kawauchi, A. (2021). Spatial graph as connected sum of a planar graph and a braid. Journal of Knot Theory and its Ramifications, 30(11), [2150077]. https://doi.org/10.1142/S0218216521500772

Vancouver

Bardakov VG, Kawauchi A. Spatial graph as connected sum of a planar graph and a braid. Journal of Knot Theory and its Ramifications. 2021 Oct 1;30(11):2150077. doi: 10.1142/S0218216521500772

Author

Bardakov, Valeriy G. ; Kawauchi, Akio. / Spatial graph as connected sum of a planar graph and a braid. In: Journal of Knot Theory and its Ramifications. 2021 ; Vol. 30, No. 11.

BibTeX

@article{fa87dd4b0a8e4220bfc8e0d70515071e,
title = "Spatial graph as connected sum of a planar graph and a braid",
abstract = "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. ",
keywords = "braid, fundamental group of spatial graph, planar graph, Spatial graph, tangle",
author = "Bardakov, {Valeriy G.} and Akio Kawauchi",
note = "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: {\textcopyright} 2021 World Scientific Publishing Company.",
year = "2021",
month = oct,
day = "1",
doi = "10.1142/S0218216521500772",
language = "English",
volume = "30",
journal = "Journal of Knot Theory and its Ramifications",
issn = "0218-2165",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "11",

}

RIS

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 -

ID: 35428039