Essential tori admitting a standard tiling

Volume 189 / 2006

Leonid Plachta Fundamenta Mathematicae 189 (2006), 195-226 MSC: 57M25, 57M15. DOI: 10.4064/fm189-3-1

Abstract

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.

Authors

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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image