Department of Mathematics

Geometry and Topology

  •  Thang Le, Georgia Tech
  •  Quantum trace map for $SL_n$ skein algebras of surfaces
  •  02/23/2021
  •  2:50 PM - 3:40 PM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Honghao Gao (gaohongh@msu.edu)

For a punctured surface there are two quantizations of the $SL_n$ character variety. The first quantization is the $SL_n$ skein algebra, and the second one is the quantization of the higher Teichmuller space. When $n=2$ Bonahon and Wong showed that there is an algebra homomorphism, called the quantum trace, from the first quantized algebra to the second one. We show for general n a similar quantum trace map exists. The construction of the $SL_n$ quantum trace is based on the theory of stated $SL_n$ skein algebra, developed in a joint work with A. Sikora, and a work of Chekhov and Shapiro.

 

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