109 citations · 467 across the 43 of their papers we have counts for
43 papers
Mutation, surface graphs, and alternating links in surfaces
Hans U. Boden, Zsuzsanna Dancso, Damian J. Lin +1
In this paper, we study alternating links in thickened surfaces in terms of the lattices of integer flows on their Tait graphs. We use this approach to give a short proof of the fi…
Mock Seifert matrices and unoriented algebraic concordance
Hans U. Boden, Homayun Karimi
A mock Seifert matrix is an integral square matrix representing the Gordon-Litherland form of a pair , where is a knot in a thickened surface and is an unoriented sp…
Examples of homology 3-spheres whose Chern-Simons function is not Morse-Bott
Hans U Boden, Christopher Herald, Paul Kirk
We construct two homology 3-spheres for which the (unperturbed) Chern-Simons function is not Morse-Bott. In one case, there is a degenerate isolated critical point. In the…
On knots that divide ribbon knotted surfaces
Hans U. Boden, Ceyhun Elmacioglu, Anshul Guha +4
We define a knot to be half ribbon if it is the cross-section of a ribbon 2-knot, and observe that ribbon implies half ribbon implies slice. We introduce the half ribbon genus of a…
Classical results for alternating virtual links
Hans U. Boden, Homayun Karimi
We extend some classical results of Bankwitz, Crowell, and Murasugi to the setting of virtual links. For instance, we show that an alternating virtual link is split if and only if…
Concordance invariants of null-homologous knots in thickened surfaces
Hans U. Boden, Homayun Karimi
Using the Gordon-Litherland pairing, one can define invariants (signature, nullity, determinant) for null-homologous links in thickened surfaces. In this paper, we…
Braid representatives minimizing the number of simple walks
Hans U. Boden, Matthew Shimoda
Given a knot, we develop methods for finding the braid representative that minimizes the number of simple walks. Such braids lead to an efficient method for computing the colored J…
The Gordon-Litherland pairing for links in thickened surfaces
Hans U. Boden, Micah Chrisman, Homayun Karimi
We extend the Gordon-Litherland pairing to links in thickened surfaces, and use it to define signature, determinant, and nullity invariants for links that bound (unoriented) spanni…
Minimal crossing number implies minimal supporting genus
Hans U. Boden, William Rushworth
A virtual link may be defined as an equivalence class of diagrams, or alternatively as a stable equivalence class of links in thickened surfaces. We prove that a minimal crossing v…
A characterization of alternating links in thickened surfaces
Hans U. Boden, Homayun Karimi
We use an extension of Gordon-Litherland pairing to thickened surfaces to give a topological characterization of alternating links in thickened surfaces. If is a closed oriente…
Adequate links in thickened surfaces and the generalized Tait conjectures
Hans U. Boden, Homayun Karimi, Adam S. Sikora
In this paper, we apply Kauffman bracket skein algebras to develop a theory of skein adequate links in thickened surfaces. We show that any alternating link diagram on a surface is…
Generalized Fishburn numbers and torus knots
Colin Bijaoui, Hans U. Boden, Beckham Myers +4
Andrews and Sellers recently initiated the study of arithmetic properties of Fishburn numbers. In this paper, we prove prime power congruences for generalized Fishburn numbers. The…
The Jones-Krushkal polynomial and minimal diagrams of surface links
Hans U. Boden, Homayun Karimi
We prove a Kauffman-Murasugi-Thistlethwaite theorem for alternating links in thickened surfaces. It states that any reduced alternating diagram of a link in a thickened surface has…
Virtual concordance and the generalized Alexander polynomial
Hans U. Boden, Micah Chrisman
We use the Bar-Natan Zh-correspondence to identify the generalized Alexander polynomial of a virtual knot with the Alexander polynomial of a two component welded link. We show that…
Virtual and welded periods of classical knots
Hans U. Boden, Andrew J. Nicas
We show that any virtual or welded period of a classical knot can be realized as a classical period. A direct consequence is that a classical knot admits only finitely many vir…
Signature and concordance of virtual knots
Hans U. Boden, Micah Chrisman, Robin Gaudreau
We introduce Tristram-Levine signatures of virtual knots and use them to investigate virtual knot concordance. The signatures are defined first for almost classical knots, which ar…
Virtual knot cobordism and bounding the slice genus
Hans U. Boden, Micah Chrisman, Robin Gaudreau
In this paper, we compute the slice genus for many low-crossing virtual knots. For instance, we show that 1295 out of 92800 virtual knots with 6 or fewer crossings are slice, and t…
Alexander invariants of periodic virtual knots
Hans U. Boden, Andrew J. Nicas, Lindsay White
We show that every periodic virtual knot can be realized as the closure of a periodic virtual braid and use this to study the Alexander invariants of periodic virtual knots. If …
Concordance group of virtual knots
Hans U. Boden, Matthias Nagel
We study concordance of virtual knots. Our main result is that a classical knot K is virtually slice if and only if it is classically slice. From this we deduce that the concordanc…
The SU(2) Casson-Lin invariant of the Hopf link
Hans U. Boden, Christopher M. Herald
We compute the Casson-Lin invariant for the Hopf link and determine the sign in the formula of Harper and Saveliev relating this invariant to the linking number.
The SU(N) Casson-Lin invariants for links
Hans U. Boden, Eric Harper
We introduce the Casson-Lin invariants for links in with more than one component. Writing , we require as input an -tuple $…
Virtual knot groups and almost classical knots
Hans U. Boden, Robin Gaudreau, Eric Harper +2
We define a group-valued invariant of virtual knots and relate it to various other group-valued invariants of virtual knots, including the extended group of Silver-Williams and the…
Bridge numbers for virtual and welded knots
Hans U. Boden, Anne Isabel Gaudreau
Using Gauss diagrams, one can define the virtual bridge number and the welded bridge number invariants of virtual and welded knots with ${\rm wb}(K) \l…
The SL(2,C) Casson invariant for knots and the -polynomial
Hans U. Boden, Cynthia L. Curtis
In this paper, we extend the definition of the Casson invariant to arbitrary knots in integral homology 3-spheres and relate it to the -degree of the $\wideha…