1 citations · 1 across the 1 of their papers we have counts for
8 papers
Knots with unique minimal genus Seifert surface and depth of knots
Mark Brittenham
We describe a procedure for creating infinite families of hyperbolic knots having unique minimal genus Seifert surface. A large subset of these knots have the further property that…
Tautly foliated 3-manifolds with no R-covered foliations
Mark Brittenham
A foliation of a manifold M is called R-covered if its lift to the universal cover of M has space of leaves R. We show that there are many graph manifolds which admit taut foliatio…
The classification of exceptional Dehn surgeries on 2-bridge knots
Mark Brittenham, Ying-Qing Wu
We will classify all exceptional Dehn surgeries on 2-bridge knots according to whether they produce reducible, toroidal, or small Seifert fibered manifolds.
Free Seifert surfaces and disk decompositions
Mark Brittenham
A Seifert surface F for a knot K is disk decomposable if there is a taut sutured manifold heirarchy for the complement of F, whose decomposing surfaces are all disks. It follows th…
Free genus one knots with large volume
Mark Brittenham
A Seifert surface F for a knot K is free if the complement of F is a handlebody (i.e., has free fundamental group). The free genus of K is the minimum genus among all free Seifert…
Bounding canonical genus bounds volume
Mark Brittenham
A Seifert surface for a knot K is called canonical if it can be built by applying Seifert's algorithm to some projection of K. The canonical genus of K is the smallest genus of a s…