16 citations · 31 across the 9 of their papers we have counts for
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math.GT2018
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…
math.GT2018★ 16 cited
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…
math.GT2018★ 1 cited
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…