4 papers · 1 filter
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…
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…