Essential tori admitting a standard tiling

• Autorzy: Leonid Plachta
• Języki publikacji: EN

Abstrakty

EN

Birman and Menasco (1994) introduced and studied a class of embedded tori in closed braid complements which admit a standard tiling. The geometric description of the tori from this class was not complete. Ng showed (1988) that each essential torus in a closed braid complement which admits a standard tiling possesses a staircase tiling pattern.
In this paper, we introduce and study the so-called longitude-meridional patterns for essential tori admitting a standard tiling. A longitude-meridional pattern of an essential torus can be derived from the corresponding tiled torus and carries a portion of geometric information about the embedded torus. We also study the interplay between the geometry of essential embedded tori and combinatorics of the corresponding tiled tori.

Kategorie tematyczne

• 57M25: Knots and links in S 3
• 57M15: Relations with graph theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 189
• Numer: 3
• Strony: 195-226

Daty

wydano

2006

Twórcy

autor

Leonid Plachta

• Institute of Applied Problems, of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 79060 Naukova 3b, Lviv, Ukraine
• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland

Identyfikatory

DOI

10.4064/fm189-3-1