Geodesic
Essential tori admitting a standard tiling
Leonid Plachta1
1 Institute 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
Fundamenta Mathematicae, Tome 189 (2006) no. 3, pp. 195-226

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/fm189-3-1
Keywords: birman menasco introduced studied class embedded tori closed braid complements which admit standard tiling geometric description tori class complete showed each essential torus closed braid complement which admits standard tiling possesses staircase tiling pattern paper introduce study so called longitude meridional patterns essential tori admitting standard tiling longitude meridional pattern essential torus derived corresponding tiled torus carries portion geometric information about embedded torus study interplay between geometry essential embedded tori combinatorics corresponding tiled tori

Leonid Plachta 1

1 Institute 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 
@article{10_4064_fm189_3_1,
     author = {Leonid Plachta},
     title = {Essential tori admitting a standard tiling},
     journal = {Fundamenta Mathematicae},
     pages = {195--226},
     publisher = {mathdoc},
     volume = {189},
     number = {3},
     year = {2006},
     doi = {10.4064/fm189-3-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm189-3-1/}
}
TY  - JOUR
AU  - Leonid Plachta
TI  - Essential tori admitting a standard tiling
JO  - Fundamenta Mathematicae
PY  - 2006
SP  - 195
EP  - 226
VL  - 189
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm189-3-1/
DO  - 10.4064/fm189-3-1
LA  - en
ID  - 10_4064_fm189_3_1
ER  - 
%0 Journal Article
%A Leonid Plachta
%T Essential tori admitting a standard tiling
%J Fundamenta Mathematicae
%D 2006
%P 195-226
%V 189
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm189-3-1/
%R 10.4064/fm189-3-1
%G en
%F 10_4064_fm189_3_1
Leonid Plachta. Essential tori admitting a standard tiling. Fundamenta Mathematicae, Tome 189 (2006) no. 3, pp. 195-226. doi: 10.4064/fm189-3-1

Cité par Sources :