Matematyka Dyskretna (prowadzone przez Mariusza Woźniaka)
We wtorek, 24 lutego 2004 roku,
o godzinie 12:45
w sali 304, łącznik
A-3-A-4, A G H
Leonid Plachta
(IAPMM of NAS of Ukraine)
wygłosi referat pod tytułem:
Essential tori admitting standard tiling:
The combinatorics
Birman and Menasco (1994) introduced and studied a class
of embedded tori in closed braid complements which admit standard
tiling. The geometric description of tori from this class was not
complete. The study of geometric properties of such tori have been
reduced in much to the study of the corresponding combinatorial
patterns, called the tiled tori. As combinatorial object, a tiled
torus is a regular graph of valence embedded in a torus, with
all the faces being rectangular tiles, and enhanced with some
additional combinatorial data. In this talk, we consider the tiled
tori as combinatorial objects in a systematic way and study their
properties.
Ng showed (1988) that each essential torus in a closed braid
complement which admits standard tiling possesses a staircase
tiling pattern. In this talk, we modify staircase patterns and
introduce the so-called
longitude-meridional patterns for tori from the given class. Both
the patterns represent actually the tiled tori in the sense mentioned
above. There is a preference in the choice of a longitude-meridional
pattern: it can be derived from the corresponding tiled torus
(tiling) and carries a portion of geometric information about the
embedded torus.
We also consider the interplay
between the geometry of essential embedded tori and combinatorics
of the corresponding tiled tori. Some open questions are posed and
discussed.
embedded in a torus, with
all the faces being rectangular tiles, and enhanced with some
additional combinatorial data. In this talk, we consider the tiled
tori as combinatorial objects in a systematic way and study their
properties.
Ng showed (1988) that each essential torus in a closed braid
complement which admits standard tiling possesses a staircase
tiling pattern. In this talk, we modify staircase patterns and
introduce the so-called
longitude-meridional patterns for tori from the given class. Both
the patterns represent actually the tiled tori in the sense mentioned
above. There is a preference in the choice of a longitude-meridional
pattern: it can be derived from the corresponding tiled torus
(tiling) and carries a portion of geometric information about the
embedded torus.
We also consider the interplay
between the geometry of essential embedded tori and combinatorics
of the corresponding tiled tori. Some open questions are posed and
discussed.