Special Issue: 2013 TAPU Workshop on Knot Theory and Related TopicsNo Access

Quantum enhancements of involutory birack counting invariants

Sam Nelson

Department of Mathematical Sciences, Claremont McKenna College, 850 Columbia Ave., Claremont, CA 91711, USA

Search for more papers by this author

and

Veronica Rivera

Department of Mathematical Sciences, Claremont McKenna College, 850 Columbia Ave., Claremont, CA 91711, USA

Search for more papers by this author

https://doi.org/10.1142/S0218216514600062Cited by:5 (Source: Crossref)

Abstract

The involutory birack counting invariant is an integer-valued invariant of unoriented tangles defined by counting homomorphisms from the fundamental involutory birack of the tangle to a finite involutory birack over a set of framings modulo the birack rank of the labeling birack. In this first of an anticipated series of several papers, we enhance the involutory birack counting invariant with quantum weights, which may be understood as tangle functors of involutory birack-labeled unoriented tangles.

Keywords:

AMSC: 57M27, 57M25

References

S. Aksoy and S. Nelson, Bikei, Involutory Biracks and unoriented link invariants, preprint (2011) , arXiv:1102.1473 . Google Scholar
N. Andruskiewitsch and M. Graña , Adv. Math. 178 , 177 ( 2003 ) . Crossref, Web of Science, Google Scholar
J. S. Carter et al. , Trans. Amer. Math. Soc. 355 , 3947 ( 2003 ) . Crossref, Web of Science, Google Scholar
M. Elhamdadi and S. Nelson , Hiroshima Math. J. 42 , 127 ( 2012 ) . Crossref, Web of Science, Google Scholar
R. Fenn , M. Jordan-Santana and L. Kauffman , Topol. Appl. 145 , 157 ( 2004 ) . Crossref, Web of Science, Google Scholar
R. Fenn and C. Rourke , J. Knot Theory Ramifications 1 , 343 ( 1992 ) . Link, Google Scholar
R. Fenn , C. Rourke and B. Sanderson , Appl. Categ. Structures 3 , 321 ( 1995 ) . Crossref, Web of Science, Google Scholar
P. J. Freyd and D. N. Yetter , Adv. Math. 77 , 156 ( 1989 ) . Crossref, Web of Science, Google Scholar
D. Joyce , J. Pure Appl. Algebra 23 , 37 ( 1982 ) . Crossref, Web of Science, Google Scholar
L. H. Kauffman and D. Radford , Contemp. Math. 318 , 113 ( 2003 ) . Crossref, Google Scholar
S. V. Matveev , Math. USSR, Sb. 47 , 73 ( 1984 ) . Crossref, Google Scholar
S. Nelson, Link invariants from finite biracks, preprint (2010) , arXiv:1002.3842 . Google Scholar
S. Sawin , Bull. Amer. Math. Soc. 33 , 413 ( 1996 ) . Crossref, Web of Science, Google Scholar
M. Takasaki , Tohoku Math. J. 49 , 143 ( 1943 ) . Google Scholar