3 citations · 3 across the 5 of their papers we have counts for
8 papers
Seifert fibered surgeries which do not arise from primitive/Seifert-fibered constructions
Thomas W. Mattman, Katura Miyazaki, Kimihiko Motegi
We construct two infinite families of knots each of which admits a Seifert fibered surgery with none of these surgeries coming from Dean's primitive/Seifert-fibered construction. T…
Ribbonlength of torus knots
Brooke Brennan, Thomas W. Mattman, Roberto Raya +1
Using Kauffman's model of flat knotted ribbons, we demonstrate how all regular polygons of at least seven sides can be realised by ribbon constructions of torus knots. We calculate…
Bounds on the Crosscap Number of Torus Knots
Thomas W. Mattman, Owen Sizemore
For a torus knot K, we bound the crosscap number c(K) in terms of the genus g(K) and crossing number n(K): c(K) \leq [(g(K)+9)/6] and c(K) \leq [(n(K) + 16)/12]. The (6n-2,3) torus…
Intrinsic knotting and linking of almost complete partite graphs
Thomas W. Mattman, Ryan Ottman, Matt Rodrigues
We classify graphs that are 0, 1, or 2 edges short of being complete partite graphs with respect to intrinsic linking and intrinsic knotting. In addition, we classify intrinsic kno…
Exceptional surgery and boundary slopes
Masaharu Ishikawa, Thomas W. Mattman, Koya Shimokawa
Let X be a norm curve in the SL(2,C)-character variety of a knot exterior M. Let t = || b || / || a || be the ratio of the Culler-Shalen norms of two distinct non-zero classes a, b…
The Culler-Shalen seminorms of the (-3,3,4) pretzel knot
Thomas W. Mattman
We describe a method to compute the Culler-Shalen seminorms of a knot, using the (-3,3,4) pretzel knot as an illustrative example. We deduce that the SL2(C)-character variety of th…