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 (

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.



Department of Mathematics
Michigan State University
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East Lansing, MI 48824

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