Essential tori admitting a standard tiling

Leonid Plachta

Fundamenta Mathematicae (2006)

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

Abstract

top
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

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.