JEDNOSTKA NAUKOWA KATEGORII A+

Climbing a Legendrian mountain range without stabilization

Tom 100 / 2014

Douglas J. LaFountain, William W. Menasco Banach Center Publications 100 (2014), 179-196 MSC: 57M25, 57R17. DOI: 10.4064/bc100-0-10

Streszczenie

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.

Autorzy

  • Douglas J. LaFountainDepartment of Mathematics
    Western Illinois University
    USA
    e-mail
  • William W. MenascoDepartment of Mathematics
    University at Buffalo
    USA
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek