Essential tori admitting a standard tiling

Leonid Plachta

Fundamenta Mathematicae (2006)

  • Volume: 189, Issue: 3, page 195-226
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Leonid Plachta. "Essential tori admitting a standard tiling." Fundamenta Mathematicae 189.3 (2006): 195-226. <http://eudml.org/doc/283061>.

@article{LeonidPlachta2006,
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. },
author = {Leonid Plachta},
journal = {Fundamenta Mathematicae},
keywords = {braid; link; essential torus; tiled torus; combinatorial meridian},
language = {eng},
number = {3},
pages = {195-226},
title = {Essential tori admitting a standard tiling},
url = {http://eudml.org/doc/283061},
volume = {189},
year = {2006},
}

TY - JOUR
AU - Leonid Plachta
TI - Essential tori admitting a standard tiling
JO - Fundamenta Mathematicae
PY - 2006
VL - 189
IS - 3
SP - 195
EP - 226
AB - 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.
LA - eng
KW - braid; link; essential torus; tiled torus; combinatorial meridian
UR - http://eudml.org/doc/283061
ER -

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