Ryan Blair
High Distance Bridge Surfaces.
Wed, 03/21/2012 - 15:01 — SomNambulAuthors: Maggy Tomova, Ryan Blair, Michael Yoshizawa
Subjects: Geometric Topology
AbstractGiven integers b, c, g, and n, we construct a manifold M containing a
c-component link L so that there is a bridge surface Sigma for (M,L) of genus g
that intersects L in 2b points and has distance at least n.- Read more
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A decomposition theorem for higher rank Coxeter groups.
Fri, 07/23/2010 - 15:01 — SomNambulAuthors: Ryan Blair, Ryan Ottman
Subjects: Group Theory
AbstractIn this paper, we show that any Coxeter graph which defines a higher rank
Coxeter group must have disjoint induced subgraphs each of which defines a
hyperbolic or higher rank Coxeter group. We then use this result to demonstrate
several classes of Coxeter graphs which define hyperbolic Coxeter groups.Companions of the unknot and width additivity.
Mon, 08/31/2009 - 17:16 — SomNambulAuthors: Maggy Tomova, Ryan Blair
Subjects: Geometric Topology
AbstractIt has been conjectured that for knots $K$ and $K'$ in $S^3$, $w(K#K')=
w(K)+w(K')-2$. Scharlemann and Thompson have proposed potential counterexamples
to this conjecture. For every $n$, they proposed a family of knots ${K^n_i}$
for which they conjectured that $w(B^n#K^n_i)=w(K^n_i)$ where $B^n$ is a bridge
number $n$ knot. We show that for $n>2$ none of the knots in ${K^n_i}$ produces
such counterexamples.
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