Climbing a Legendrian mountain range without stabilization

Douglas J. LaFountain, and William W. Menasco. "Climbing a Legendrian mountain range without stabilization." Banach Center Publications 100.1 (2014): 179-196. <http://eudml.org/doc/281815>.

@article{DouglasJ2014,
abstract = {We introduce a new braid-theoretic framework with which to understand the Legendrian and transversal classification of knots, namely a Legendrian Markov Theorem without Stabilization which induces an associated transversal Markov Theorem without Stabilization. We establish the existence of a nontrivial knot-type specific Legendrian and transversal MTWS by enhancing the Legendrian mountain range for the (2,3)-cable of a (2,3)-torus knot provided by Etnyre and Honda, and showing that elementary negative flypes allow us to move toward maximal tb value without having to use Legendrian stabilization. In doing so we obtain new ways to visualize convex tori and Legendrian divides and rulings, using tilings and braided rectangular diagrams.},
author = {Douglas J. LaFountain, William W. Menasco},
journal = {Banach Center Publications},
keywords = {knot; links; braids; stabilization; Markov's theorem; braid foliations; flypes},
language = {eng},
number = {1},
pages = {179-196},
title = {Climbing a Legendrian mountain range without stabilization},
url = {http://eudml.org/doc/281815},
volume = {100},
year = {2014},
}

TY - JOUR
AU - Douglas J. LaFountain
AU - William W. Menasco
TI - Climbing a Legendrian mountain range without stabilization
JO - Banach Center Publications
PY - 2014
VL - 100
IS - 1
SP - 179
EP - 196
AB - We introduce a new braid-theoretic framework with which to understand the Legendrian and transversal classification of knots, namely a Legendrian Markov Theorem without Stabilization which induces an associated transversal Markov Theorem without Stabilization. We establish the existence of a nontrivial knot-type specific Legendrian and transversal MTWS by enhancing the Legendrian mountain range for the (2,3)-cable of a (2,3)-torus knot provided by Etnyre and Honda, and showing that elementary negative flypes allow us to move toward maximal tb value without having to use Legendrian stabilization. In doing so we obtain new ways to visualize convex tori and Legendrian divides and rulings, using tilings and braided rectangular diagrams.
LA - eng
KW - knot; links; braids; stabilization; Markov's theorem; braid foliations; flypes
UR - http://eudml.org/doc/281815
ER -