Arnold' seminar, Moscow University
September 30, 2003

On tori triangulation associated with multidimensional
continued fractions for algebraic irrationalities.
Oleg Karpenkov.

Abstract:
We consider one of the most well known generalizations for ordinary continued
fractions to the multidimensional case.
Preliminary we recall the notions of multidimensional continued fractions
for algebraic irrationalities, sails, triangulations, and natural
equivalence classes for them.
The first natural question here is to find some natural family of
continued fractions that represent these equivalence classes.
We present some new results in this direction.
Further we show some examples of two-dimensional continued fractions
for cubic irrationalities and discuss some arising questions.

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