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 = {Zhiguo and Li and zhiguolee@mail.dlut.edu.cn and 5476 and Department of Mathematics, Dalian University of Technology, Dalian, Liaoning, 116024 and Zhiguo Li and Fengchun and Lei and and 5415 and School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024 and Fengchun Lei and Zhi and Chen and and 5480 and Department of Mathematics, Hefei University of Technology, Hefei, 230009 and Zhi Chen and Jie and Wu and and 5481 and googleDepartment of Mathematics, National University of Singapore, Singapore and Jie Wu}, 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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