Volume 33, Issue 2
On Fundamental Group of a Certain Class of Welded Knots

Commun. Math. Res., 33 (2017), pp. 177-184.

Published online: 2019-11

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• Abstract

In this paper, a certain class of welded knots $K_{2n}$ is considered. By calculating the commutators subgroup of fundamental group $G_n$ of welded knot $K_{2n}$, $n ∈$ Z+, we show that these welded knots are not equivalent to each other and they are all not classical knots. Secondly, we study some properties of $G_n$ and obtain that $G_n$ is linear, residually finite and Hopfian.

• Keywords

welded knot, fundamental group, Dihedral group, linear group

57M25, 57M27

zhiguolee@mail.dlut.edu.cn (Zhiguo Li)

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@Article{CMR-33-177, author = {Li , Zhiguo and Lei , Fengchun and Chen , Zhi and Wu , Jie}, title = {On Fundamental Group of a Certain Class of Welded Knots}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {33}, number = {2}, pages = {177--184}, abstract = {

In this paper, a certain class of welded knots $K_{2n}$ is considered. By calculating the commutators subgroup of fundamental group $G_n$ of welded knot $K_{2n}$, $n ∈$ Z+, we show that these welded knots are not equivalent to each other and they are all not classical knots. Secondly, we study some properties of $G_n$ and obtain that $G_n$ is linear, residually finite and Hopfian.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2017.02.09}, url = {http://global-sci.org/intro/article_detail/cmr/13397.html} }
TY - JOUR T1 - On Fundamental Group of a Certain Class of Welded Knots AU - Li , Zhiguo AU - Lei , Fengchun AU - Chen , Zhi AU - Wu , Jie JO - Communications in Mathematical Research VL - 2 SP - 177 EP - 184 PY - 2019 DA - 2019/11 SN - 33 DO - http://doi.org/10.13447/j.1674-5647.2017.02.09 UR - https://global-sci.org/intro/article_detail/cmr/13397.html KW - welded knot, fundamental group, Dihedral group, linear group AB -

In this paper, a certain class of welded knots $K_{2n}$ is considered. By calculating the commutators subgroup of fundamental group $G_n$ of welded knot $K_{2n}$, $n ∈$ Z+, we show that these welded knots are not equivalent to each other and they are all not classical knots. Secondly, we study some properties of $G_n$ and obtain that $G_n$ is linear, residually finite and Hopfian.

Zhiguo Li, Fengchun Lei, Zhi Chen & Jie Wu. (2019). On Fundamental Group of a Certain Class of Welded Knots. Communications in Mathematical Research . 33 (2). 177-184. doi:10.13447/j.1674-5647.2017.02.09
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