Department of Mathematics

Geometry and Topology

  •  Daniel López Neumann, Indiana University
  •  Twisting quantum invariants via Fox calculus
  •  10/05/2021
  •  4:00 PM - 5:00 PM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Honghao Gao (gaohongh@msu.edu)

The Reshetikhin-Turaev invariants of a knot are topological invariants built through the representation theory of certain Hopf algebras, such as quantum groups. In the early 2000s, Turaev introduced a G-graded version of this construction that produces invariants of knots equipped with representations of their fundamental group into the group G. This talk will be about a special case of the G-graded construction. We will show that a graded Drinfeld double construction leads to Reshetikhin-Turaev invariants of knots which are “twisted” via the usual Fox calculus. This construction applies to a wide class of Hopf algebras, and in the case of an exterior algebra, it specializes to the twisted Reidemeister torsion of the complement of a knot.

 

Contact

Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science