Abstract
Twisted knot theory introduced by M. Bourgoin is a generalization of knot theory. It leads us to the notion of twisted virtual braids. In this paper we show theorems for twisted links corresponding to the Alexander theorem and the Markov theorem in knot theory. We also provide a group presentation and a reduced group presentation of the twisted virtual braid group.
Acknowledgments
K. Negi would like to thank the University Grants Commission(UGC), India, for Research Fellowship with NTA Ref.No.191620008047. M. Prabhakar acknowledges the support given by the Science and Engineering Board(SERB), Department of Science $&$ Technology, Government of India under grant-in-aid Mathematical Research Impact Centric Support(MATRICS) with F.No.MTR/2021/00394. This work was partially supported by the FIST program of the Department of Science and Technology, Government of India, Reference No. SR/FST/MS-I/2018/22(C), and was supported by JSPS KAKENHI Grant Number JP19H01788.
Citation
Komal Negi. Madeti Prabhakar. Seiichi Kamada. "Twisted virtual braids and twisted links." Osaka J. Math. 61 (4) 569 - 590, October 2024.
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