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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm189-3-1,
author = {Leonid Plachta},
title = {Essential tori admitting a standard tiling},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {195-226},
zbl = {1099.57009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm189-3-1}
}
Leonid Plachta. Essential tori admitting a standard tiling. Fundamenta Mathematicae, Tome 189 (2006) pp. 195-226. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm189-3-1/