On Fundamental Group of a Certain Class of Welded Knots

Authors

  • Zhiguo Li Department of Mathematics, Dalian University of Technology, Dalian, Liaoning, 116024
  • Fengchun Lei School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024
  • Zhi Chen Department of Mathematics, Hefei University of Technology, Hefei, 230009
  • Jie Wu googleDepartment of Mathematics, National University of Singapore, Singapore

DOI:

https://doi.org/10.13447/j.1674-5647.2017.02.09

Keywords:

welded knot, fundamental group, Dihedral group, linear group

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. 

Downloads

Published

2019-12-16

Abstract View

  • 35949

Pdf View

  • 2802

Issue

Vol. 33 No. 2 (2017)

Section

Articles

How to Cite

On Fundamental Group of a Certain Class of Welded Knots. (2019). Communications in Mathematical Research, 33(2), 177-184. https://doi.org/10.13447/j.1674-5647.2017.02.09