Alexander- and Markov-type theorems for virtual trivalent braids-Reference-Cited by-同舟云学术

Alexander- and Markov-type theorems for virtual trivalent braids

Published:2019-01 Issue:01 Volume:28 Page:1950003
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

Caprau Carmen¹^ORCID,Dirdak Abigayle¹,Post Rita²,Sawyer Erica³

Affiliation:

1. Department of Mathematics, California State University, Fresno, 5245 North Backer Avenue M/S PB 108, Fresno, CA 93740, USA

2. Department of Mathematics, University of Wisconsin-Eau Claire, 124 Garfield Avenue, Eau Claire, WI 54701, USA

3. Department of Mathematics, The Evergreen State College, 2700 Evergreen Parkway NW, Olympia, WA 98505, USA

Abstract

We prove Alexander- and Markov-type theorems for virtual spatial trivalent graphs and virtual trivalent braids. We provide two versions for the Markov-type theorem: one uses an algebraic approach similar to the case of classical braids and the other one is based on [Formula: see text]-moves.

Funder

National Science Foundation

Simons Foundation

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216519500032

Reference11 articles.

1. A Lemma on Systems of Knotted Curves

2. Virtual singular braids and links

3. The Markov theorems for spatial graphs and handlebody-knots with Y-orientations

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