3 citations · 7 across the 12 of their papers we have counts for
17 papers
Finite quotients of spherical Artin groups
Sam Hughes, Thomas Ng, Kaitlin Ragosta +2
We show the smallest non-abelian quotients of spherical and affine Artin groups are isomorphic to the smallest non-abelian quotients of the corresponding Coxeter groups. We deduce…
Combinatorial Goussarov-Polyak-Viro Formulas for the Linking Number and Low Degree Coefficients of the Conway Polynomial
Nancy Scherich, Nathaniel Song
The linking number and coefficients of the Conway polynomial are two examples of finite type invariants. Goussarov-Polyak-Viro proved that any finite type knot invariant can be com…
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…
Goldman-Turaev formality from the Kontsevich integral
Dror Bar-Natan, Zsuzsanna Dancso, Tamara Hogan +2
We present a new solution to the formality problem for the framed Goldman--Turaev Lie bialgebra, constructing Goldman-Turaev homomorphic expansions (formality isomorphisms) from th…
Danceability of twisted virtual knots
Sol Addison, Nancy Scherich, Lila Snodgrass
Over the years, several Bridges papers have delved into the concept of danceability of a knot diagram. Inspired by dancing on non-orientable surfaces, in this paper, we expand danc…
Danceability, A New Definition of Bridge Index
Sol Addison, Sarah Blackwell, Puttipong Pongtanapaisan +3
There are many commonly known definitions of the bridge index coming from combinatorial knot theory, Morse theory, geometry, and algebra. In this paper, we prove that the danceabil…
Searching for non-order-preserving braids algorithmically
Jonathan Johnson, Nancy Scherich, Hannah Turner
An -strand braid is order-preserving if its action on the free group preserves some bi-order of . A braid is order-preserving if and only if the link obtained…
Computing Finite Type Invariants Efficiently
Dror Bar-Natan, Itai Bar-Natan, Iva Halacheva +1
We describe an efficient algorithm to compute finite type invariants of type by first creating, for a given knot with crossings, a look-up table for all subdiagrams of…
Danceability, Directed by Braid Index
Sol Addison, Nancy Scherich, Lila Snodgrass
Schaffer introduced the concept of danceability of a knot diagram. In this paper, we expand upon Schaffer's ideas to create a danceability knot invariant and show that this invaria…
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…
Large 1-systems of Curves in Non-orientable Surfaces
Sarah Ruth Nicholls, Nancy Scherich, Julia Shneidman
A longstanding avenue of research in orientable surface topology is to create and enumerate collections of curves in surfaces with certain intersection properties. We look for simi…
Yarn Ball Knots and Faster Computations
Dror Bar-Natan, Itai Bar-Natan, Iva Halacheva +1
We make use of the 3D nature of knots and links to find savings in computational complexity when computing knot invariants such as the linking number and, in general, most finite t…
An Invariant of Virtual Trivalent Spatial Graphs
Evan Carr, Nancy Scherich, Sherilyn Tamagawa
We create an invariant of virtual Y-oriented trivalent spatial graphs using colorings by virtual Niebrzydowski algebras. This paper generalizes the color invariants using virtual t…
Finite image homomorphisms of the braid group and its generalizations
Nancy Scherich, Yvon Verberne
Using totally symmetric sets, Chudnovsky, Kordek, Li, and Partin gave a superexponential lower bound on the cardinality of non-abelian finite quotients of the braid group. In this…
Discrete Real Specializations of Sesquilinear Representations of the Braid Groups
Nancy C. Scherich
This paper gives a process for finding discrete real specializations of sesquilinear representations of the braid groups using Salem numbers. This method is applied to the Jones an…
Ribbon 2-Knots, , and Duflo's Theorem for Arbitrary Lie Algebras
Dror Bar-Natan, Zsuzsanna Dancso, Nancy Scherich
We explain a direct topological proof for the multiplicativity of Duflo isomorphism for arbitrary finite dimensional Lie algebras, and derive the explicit formula for the Duflo map…
Classification of the Discrete Real Specializations of the Burau Representation of
Nancy Scherich
This classification is found by analyzing the action of a normal subgroup of as hyperbolic isometries. This paper gives an example of an unfaithful specialization of the Bura…