6 citations · 15 across the 15 of their papers we have counts for
16 papers
Fundamentals of cubic skein modules
Rhea Palak Bakshi, Anthony Christiana, Huizheng Guo +6
Over the past thirty-seven years, the study of linear and quadratic skein modules has produced a rich and far-reaching skein theory, intricately connected to diverse areas of mathe…
Temperley-Lieb Categories on Non-Orientable Surfaces
Dionne Ibarra, Gabriel Montoya-Vega, Benjamin Morris
In this paper we present the construction of a skeletal diagram category, which we call the square with bands category. This category extends the Temperley-Lieb (TL) category, wher…
Chebyshev polynomials and Gram determinants from the Möbius band
Anthony Christiana, Dionne Ibarra, Gabriel Montoya-Vega
This article explores the connection between Chebyshev polynomials and knot theory, specifically in relation to Gram determinants. We reveal intriguing formulae involving the Cheby…
A robot that unknots knots
Connie On Yu Hui, Dionne Ibarra, Louis H. Kauffman +4
Consider a robot that remembers only the starting position and walks along a knot once on a knot diagram, switching every undercrossing it meets until it returns to the starting po…
The Montesinos-Nakanishi 3-move conjecture for links up to 20 crossings
Rhea Palak Bakshi, Benjamin A. Burton, Huizheng Guo +4
Yasutaka Nakanishi formulated the following conjecture in 1981: every link is 3-move equivalent to a trivial link. While the conjecture was proved for several specific cases, it re…
Independence complexes of circle graphs
Rhea Palak Bakshi, Ali Guo, Dionne Ibarra +4
Independence complexes of circle graphs are purely combinatorial objects. However, when constructed from some diagram of a link , they reveal topological properties of , more…
A Study of Gram Determinants in Knot Theory
Dionne Ibarra, Gabriel Montoya-Vega
Historically originated as a sub-field of topology, knot theory is an active area of mathematical investigation that has strong connections with a diverse set of scientific fields…
A lower bound for the volumes of modular link complements
Connie On Yu Hui, Dionne Ibarra, José Andrés Rodríguez Migueles
Every finite collection of oriented closed geodesics in the modular surface has a canonically associated link in its unit tangent bundle coming from the periodic orbits of the geod…
Exploring unimodality of the plucking polynomial with delay function
Dionne Ibarra, Alex Landry, Gabriel Montoya-Vega +1
The plucking polynomial is an invariant of rooted trees with connections to knot theory. The polynomial was constructed in 2014 as a tool to analyze lattice crossings after taking…
On a new Gram determinant from the Möbius band
Dionne Ibarra, Gabriel Montoya-Vega
Gram determinants earned traction among knot theorists after E. Witten's presumption about the existence of a 3-manifold invariant connected to the Jones polynomial. Triggered by t…
Jones-Wenzl Idempotents in the Twisted -bundle over the Möbius band
Dionne Ibarra
The Jones-Wenzl idempotent plays a vital role in quantum invariants of -manifolds and the colored Jones polynomial; it also serves as a useful tool for simplifying computations…
A note on a short proof of the parallelizability of orientable -manifolds
Dionne Ibarra
We survey, complete, and modify a proof, involving knot theory, of Stiefel's theorem that all orientable -manifolds are parallelizable. The completion of the proof is done by us…
On framings of links in 3-manifolds
Rhea Palak Bakshi, Dionne Ibarra, Gabriel Montoya-Vega +2
We show that the only way of changing the framing of a link by ambient isotopy in an oriented -manifold is when the manifold has a properly embedded non-separating . This c…
A Generalization of the Gram determinant of type A
Rhea Palak Bakshi, Dionne Ibarra, Sujoy Mukherjee +1
The Gram determinant of type was introduced by Lickorish in his work on invariants of 3 - manifolds. We generalize the theory of the Gram determinant of type by evaluating,…
Schur Multipliers and Second Quandle Homology
Rhea Palak Bakshi, Dionne Ibarra, Sujoy Mukherjee +2
We define a map from second quandle homology to the Schur multiplier and examine its properties. Furthermore, we express the second homology of Alexander quandles in terms of exter…
On a state model for the SO(2n) Kauffman polynomial
Carmen Caprau, David Heywood, Dionne Ibarra
F. Jaeger presented the two-variable Kauffman polynomial of an unoriented link L as a weighted sum of HOMFLY-PT polynomials of oriented links associated with L. Murakami, Ohtsuki a…