26 citations · 59 across the 18 of their papers we have counts for
22 papers
On the arc index and Turaev genus of a link
Álvaro Del Valle Vílchez, Adam M. Lowrance
We compute the arc index of an adequate link and establish bounds on the arc index of the closure of a positive 3-braid. We also conjecture an inequality between the crossing numbe…
A characterization of adequate Turaev genus one links
Khaled Qazaqzeh, Nafaa Chbili, Adam M. Lowrance
We prove that a link is adequate and has Turaev genus one if and only if the span of its Jones polynomial is one less than its crossing number.
Average crosscap number of a 2-bridge knot
Moshe Cohen, Thomas Kindred, Adam M. Lowrance +2
We determine a simple condition on a particular state graph of an alternating knot or link diagram that characterizes when the unoriented genus and crosscap number coincide, extend…
Average signature and 4-genus of 2-bridge knots
Moshe Cohen, Adam M. Lowrance, Neal Madras +1
We show that the average or expected absolute value of the signatures of all 2-bridge knots with crossing number approaches . Baader, Kjuchukova, Lewark, Misev,…
The distribution of braid indices of 2-bridge knots
Tobias Clark, Jeremy Frank, Adam M. Lowrance
In this article we study the braid indices of 2-bridge knots with a fixed crossing number . We show that the average braid index of the set of -bridge knots of crossing numbe…
The distribution of genera of 2-bridge knots
Moshe Cohen, Abigail DiNardo, Adam M. Lowrance +4
The average genus of a 2-bridge knot with crossing number approaches as approaches infinity, as proven by Suzuki and Tran and independently Coh…
Near extremal Khovanov homology of Turaev genus one links
Theo Beldon, Mia DeStefano, Adam M. Lowrance +2
The Turaev surface of a link diagram is a closed, oriented surface constructed from a cobordism between the all- and all- Kauffman states of . The Turaev genus of a li…
The average genus of a 2-bridge knot is asymptotically linear
Moshe Cohen, Adam M. Lowrance
Experimental work suggests that the Seifert genus of a knot grows linearly with respect to the crossing number of the knot. In this article, we use a billiard table model for -b…
On Khovanov Homology and Related Invariants
Carmen Caprau, Nicolle González, Christine Ruey Shan Lee +3
This paper begins with a survey of some applications of Khovanov homology to low-dimensional topology, with an eye toward extending these results to homologies.…
The multi-region index of a knot
Sarah Goodhill, Adam M. Lowrance, Valeria Munoz Gonzales +2
Using region crossing changes, we define a new invariant called the multi-region index of a knot. We prove that the multi-region index of a knot is bounded from above by twice the…
Torsion in thin regions of Khovanov homology
Alex Chandler, Adam M. Lowrance, Radmila Sazdanovic +1
In the integral Khovanov homology of links, the presence of odd torsion is rare. Homologically thin links, that is links whose Khovanov homology is supported on two adjacent diagon…
Extremal Khovanov homology of Turaev genus one links
Oliver T. Dasbach, Adam M. Lowrance
The Turaev genus of a link can be thought of as a way of measuring how non-alternating a link is. A link is Turaev genus zero if and only if it is alternating, and in this viewpoin…
The 2-Factor Polynomial Detects Even Perfect Matchings
Scott Baldridge, Adam M. Lowrance, Ben McCarty
In this paper, we prove that the 2-factor polynomial, an invariant of a planar trivalent graph with a perfect matching, counts the number of 2- factors that contain the the perfect…
The Jones polynomial of an almost alternating link
Adam M. Lowrance, Dean Spyropoulos
A link is almost alternating if it is non-alternating and has a diagram that can be transformed into an alternating diagram via one crossing change. We give formulas for the first…
On the Turaev genus of torus knots
Kaitian Jin, Adam M. Lowrance, Eli Polston +1
The Turaev genus and dealternating number of a link are two invariants that measure how far away a link is from alternating. We determine the Turaev genus of a torus knot with five…
Chromatic homology, Khovanov homology, and torsion
Adam M. Lowrance, Radmila Sazdanovic
In the first few homological gradings, there is an isomorphism between the Khovanov homology of a link and the categorification of the chromatic polynomial of a graph related to th…
Turaev genus and alternating decompositions
Cody W. Armond, Adam M. Lowrance
We prove that the genus of the Turaev surface of a link diagram is determined by a graph whose vertices correspond to the boundary components of the maximal alternating regions of…
Alternating distances of knots and links
Adam M. Lowrance
An alternating distance is a link invariant that measures how far away a link is from alternating. We study several alternating distances and demonstrate that there exist families…
Turaev genus, knot signature, and the knot homology concordance invariants
Oliver T. Dasbach, Adam M. Lowrance
We give bounds on knot signature, the Ozsvath-Szabo tau invariant, and the Rasmussen s invariant in terms of the Turaev genus of the knot.
The Khovanov width of twisted links and closed 3-braids
Adam Lowrance
Khovanov homology is a bigraded Z-module that categorifies the Jones polynomial. The support of Khovanov homology lies on a finite number of slope two lines with respect to the big…
Cube diagrams and 3-dimensional Reidemeister-like moves for knots
Scott Baldridge, Adam Lowrance
In this paper we introduce a representation of knots and links called a cube diagram. We show that a property of a cube diagram is a link invariant if and only if the property is i…
On knot Floer width and Turaev genus
Adam Lowrance
To each knot one can associated its knot Floer homology , a finitely generated bigraded abelian group. In general, the nonzero ranks of these homology…