Miraculous cancellations and the quantum Frobenius for SL₃ skein modules

2024/08/31 by Vijay Higgins, Higgins, Vijay · 1 citation
Mathematics · #57K31 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2409.00351

openalex publication_date 2024/08/31 · openalex created_date 2024/09/29 · openalex updated_date 2026/07/28

Abstract

We construct a quantum Frobenius map for the SL₃ skein module of any oriented 3-manifold specialized at a root of unity, and describe the map by way of threading certain polynomials along links. The homomorphism is a higher rank version of the Chebyshev-Frobenius homomorphism of Bonahon-Wong. The strategy builds on a previous construction of the Frobenius map for SL₃ skein algebras of punctured surfaces, using the Frobenius map of Parshall-Wang for the quantum group O_q(SL₃).

Cited by

• Steinberg skein identities at roots of unity

Related

• The Chebyshev-Frobenius homomorphism for stated skein modules of 3-manifolds
• Frobenius homomorphisms for stated \rm SL_n-skein modules
• Stated skein modules of marked 3-manifolds/surfaces, a survey
• Frobenius algebras and skein modules of surfaces in 3-manifolds
• The Unicity Theorem and the center of the \rm SL₃-skein algebra