Non-semisimple quantum invariants and abelian classical shadows

2023/11/06 by Renaud Detcherry, Detcherry, Renaud
Mathematics · #Geometric and Algebraic Topology #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2311.03258

Abstract

Using the U_q^Hsl₂ non-semisimple invariants of 3-manifolds at odd roots of unity, we construct maps on the Kauffman bracket skein module at roots of unity of order twice an odd number, having any possible abelian non central character as classical shadow.

Related

• Shadows and quantum invariants
• A proof of the shadow formula for the SU(2)-Reshetikhin-Turaev-Witten invariant
• Quantum torus methods for Kauffman bracket skein modules
• Fundamentals of Kauffman bracket skein modules
• The quantum trace as a quantum non-abelianization map