29 citations · 64 across the 6 of their papers we have counts for
7 papers
Distance-balancing of cube-connected cycles graphs
Mokhtar Aouina, Hamed Karami, Douglas J. LaFountain
We show that cube-connected cycles graphs are distance-balanced, and nicely distance-balanced if and only if is even.
Embedded annuli and Jones' conjecture
Douglas J. LaFountain, William W. Menasco
We show that after stabilizations of opposite parity and braid isotopy, any two braids in the same topological link type cobound embedded annuli. We use this to prove the generaliz…
Filtered screens and augmented Teichmüller space
Douglas J. LaFountain, R. C. Penner
We study a new bordification of the decorated Teichmüller space for a multiply punctured surface F by a space of filtered screens on the surface that arises from a natural elaborat…
Legendrian and transverse cables of positive torus knots
John B. Etnyre, Douglas J. LaFountain, Bulent Tosun
In this paper we classify Legendrian and transverse knots in the knot types obtained from positive torus knots by cabling. This classification allows us to demonstrate several new…
Studying uniform thickness II: Transversely non-simple iterated torus knots
Douglas J. LaFountain
We prove that an iterated torus knot type fails the uniform thickness property (UTP) if and only if all of its iterations are positive cablings, which is precisely when an iterated…
Studying uniform thickness I: Legendrian simple iterated torus knots
Douglas J. LaFountain
We prove that the class of topological knot types that are both Legendrian simple and satisfy the uniform thickness property (UTP) is closed under cabling. An immediate application…
Climbing a Legendrian mountain range without Stabilization
Douglas J. LaFountain, William W. Menasco
We introduce a new braid-theoretic framework with which to understand the Legendrian and transversal classification of knots, namely a Legendrian Markov Theorem without Stabilizati…