5 citations · 10 across the 9 of their papers we have counts for
9 papers
Congruence Subgroups of the Virtual Braid Group
Wade Bloomquist, Alexa Goldberg, Nancy Scherich
We extend the notion of congruence subgroups of the braid group to the virtual braid group using an extension of the integral Burau representation. We prove that the level 2 congru…
Degenerations Of Skein Algebras And Quantum Traces
Wade Bloomquist, Hiroaki Karuo, Thang Lê
We introduce a joint generalization, called LRY skein algebras, of Kauffman bracket skein algebras (of surfaces) that encompasses both Roger-Yang skein algebras and stated skein al…
Quotients of braid groups by their congruence subgroups
Wade Bloomquist, Peter Patzt, Nancy Scherich
The congruence subgroups of braid groups arise from a congruence condition on the integral Burau representation . We find the image of suc…
On quotients of congruence subgroups of braid groups
Jessica Appel, Wade Bloomquist, Katie Gravel +1
The integral Burau representation provides a map from the braid group into a group of integral matrices. This allows for a definition of congruence subgroups of the braid group as…
The Chebyshev-Frobenius homomorphism for stated skein modules of 3-manifolds
Wade Bloomquist, Thang T. Q. Lê
We study the stated skein modules of marked 3-manifolds. We generalize the splitting homomorphism for stated skein algebras of surfaces to a splitting homomorphism for stated skein…
On Topological Quantum Computing With Mapping Class Group Representations
Wade Bloomquist, Zhenghan Wang
We propose an encoding for topological quantum computation utilizing quantum representations of mapping class groups. Leakage into a non-computational subspace seems to be unavoida…