16 citations · 31 across the 9 of their papers we have counts for
12 papers
Colored Jones Polynomials and the Volume Conjecture
Mark Hughes, Vishnu Jejjala, P. Ramadevi +2
Using the vertex model approach for braid representations, we compute polynomials for spin-1 placed on hyperbolic knots up to 15 crossings. These polynomials are referred to as 3-c…
Non-isotopic splitting spheres for a split link in
Mark Hughes, Seungwon Kim, Maggie Miller
We show that there exist split, orientable, 2-component surface-links in with non-isotopic splitting spheres in their complements. In particular, for non-negative integers $m…
Learning knot invariants across dimensions
Jessica Craven, Mark Hughes, Vishnu Jejjala +1
We use deep neural networks to machine learn correlations between knot invariants in various dimensions. The three-dimensional invariant of interest is the Jones polynomial ,…
Knotted handlebodies in the 4-sphere and 5-ball
Mark Hughes, Seungwon Kim, Maggie Miller
For every integer we construct 3-dimensional genus- 1-handlebodies smoothly embedded in with the same boundary, and which are defined by the same cut systems of t…
Band diagrams of immersed surfaces in 4-manifolds
Mark Hughes, Seungwon Kim, Maggie Miller
We study immersed surfaces in smooth 4-manifolds via singular banded unlink diagrams. Such a diagram consists of a singular link with bands inside a Kirby diagram of the ambient 4-…
A Reidemeister type theorem for petal diagrams of knots
Leslie Colton, Cory Glover, Mark Hughes +1
We study petal diagrams of knots, which provide a method of describing knots in terms of permutations in a symmetric group . We define two classes of moves on such permut…
Isotopies of surfaces in 4-manifolds via banded unlink diagrams
Mark C. Hughes, Seungwon Kim, Maggie Miller
In this paper, we study surfaces embedded in -manifolds. We give a complete set of moves relating banded unlink diagrams of isotopic surfaces in an arbitrary -manifold. This…
Immersed Möbius bands in knot complements and representatives of -homology classes
Mark C. Hughes, Seungwon Kim
We study the 3-dimensional immersed crosscap number of a knot, which is a nonorientable analogue of the immersed Seifert genus. We study knots with immersed crosscap number 1, and…
A neural network approach to predicting and computing knot invariants
Mark C. Hughes
In this paper we use artificial neural networks to predict and help compute the values of certain knot invariants. In particular, we show that neural networks are able to predict w…
Constructing broken Lefschetz fibrations from handle decompositions
Mark C. Hughes
We present an approach to constructing broken Lefschetz fibrations (BLFs) from a handle decomposition of a 4-manifold . Given a handle decomposition as inpu…
Braiding link cobordisms and non-ribbon surfaces
Mark C. Hughes
We define the notion of a braided link cobordism in , which generalizes Viro's closed surface braids in . We prove that any properly embedded orient…
A note on Khovanov-Rozansky -homology and ordinary Khovanov homology
Mark C. Hughes
In this note we present an explicit isomorphism between Khovanov-Rozansky -homology and ordinary Khovanov homology. This result was originally stated in Khovanov and Rozansky…