3 papers
math.GT2025
Type skein modules and transparent elements
Vijay Higgins, Haihan Wu
We study skein modules using webs. We define multivariable analogues of Chebyshev polynomials in the Type setting and use them to construct transparent elements in the…
math.GT2025
Steinberg skein identities at roots of unity
Vijay Higgins, Indraneel Tambe
We obtain a family of skein identities in the Kauffman bracket skein module which relate Frobenius elements to Jones-Wenzl projectors at roots of unity. We view these skein identit…
math.GT2024
Miraculous cancellations and the quantum Frobenius for skein modules
Vijay Higgins
We construct a quantum Frobenius map for the skein module of any oriented 3-manifold specialized at a root of unity, and describe the map by way of threading certain polynom…