Trace Digarams and Biquandle Brackets

Sam Nelson

Knots in Washington XLVI: 70th Birthday of Oleg Viro;
May 4-6, 2018
George Washington University,
Washington, DC, USA

Organizers
Valentina Harizanov (GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU)

Conference Homepage

Trace Digarams and Biquandle Brackets
by
Sam Nelson
Claremont McKenna College
Coauthors: Natsumi Oyamaguchi

Biquandle brackets are skein invariants of biquandle-colored knot and link diagrams. While originally defined using a state-sum formulation, for hand computation it is desirable to have a definition of these invariants via a recursive skein expansion, but there is a problem -- smoothings break the biquandle coloring. In this talk we show how to resolve this issue using signed trace diagrams. We find conditions on biquandle brackets to allow over- and under-pass trace moves and identify a Homflypt-style skein relation at monochromatic crossings. This is joint work with Natsumi Oyamaguchi (Shumei University, Japan).

Date received: March 24, 2018