VIRTUAL KNOT INVARIANTS FROM GROUP BIQUANDLES AND THEIR COCYCLES-Reference-Cited by-同舟云学术

VIRTUAL KNOT INVARIANTS FROM GROUP BIQUANDLES AND THEIR COCYCLES

Published:2009-07 Issue:07 Volume:18 Page:957-972
ISSN:0218-2165
Container-title:Journal of Knot Theory and Its Ramifications
language:en
Short-container-title:J. Knot Theory Ramifications

Author:

CARTER J. SCOTT¹,SILVER DANIEL S.¹,WILLIAMS SUSAN G.¹,ELHAMDADI MOHAMED²,SAITO MASAHICO²

Affiliation:

1. Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama 36688, USA

2. Department of Mathematics and Statistics, University of South Florida, Tampa, Florida 33620, USA

Abstract

A group-theoretical method, via Wada's representations, is presented to distinguish Kishino's virtual knot from the unknot. Biquandles are constructed for any group using Wada's braid group representations. Cocycle invariants for these biquandles are studied. These invariants are applied to show the non-existence of Alexander numberings and checkerboard colorings.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218216509007269

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