A cohomology theory for colored tangles

• Autorzy: Carmen Caprau
• Języki publikacji: EN

Abstrakty

EN

We employ the sl(2) foam cohomology to define a cohomology theory for oriented framed tangles whose components are labeled by irreducible representations of $U_q(sl(2))$. We show that the corresponding colored invariants of tangles can be assembled into invariants of bigger tangles. For the case of knots and links, the corresponding theory is a categorification of the colored Jones polynomial, and provides a tool for efficient computations of the resulting colored invariant of knots and links. Our theory is defined over the Gaussian integers ℤ[i] (and more generally over ℤ[i][a,h], where a,h are formal parameters), and enhances the existing categorifications of the colored Jones polynomial.

Kategorie tematyczne

• 57M27: Invariants of knots and 3-manifolds
• 57M25: Knots and links in S 3
• 18G60: Other (co)homology theories

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2014
• Tom: 100
• Numer: 1
• Strony: 13-25

Daty

wydano

2014

Twórcy

autor

Carmen Caprau

• Department of Mathematics, California State University, Fresno, CA 93740, USA

Identyfikatory

DOI

10.4064/bc100-0-1