Climbing a Legendrian mountain range without stabilization

• Autorzy: Douglas J. LaFountain , William W. Menasco
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57M25: Knots and links in S 3
• 57R17: Symplectic and contact topology

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2014
• Tom: 100
• Numer: 1
• Strony: 179-196

Daty

wydano

2014

Twórcy

autor

Douglas J. LaFountain

• Department of Mathematics, Western Illinois University, USA

autor

William W. Menasco

• Department of Mathematics, University at Buffalo, USA

Identyfikatory

DOI

10.4064/bc100-0-10