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Дискретная и вычислительная геометрия
12 апреля 2016 г. 13:45, г. Москва, ИППИ РАН, Большой Каретный переулок, 19, ауд. 307
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[Topology and combinatorics of “unavoidable complexes”]
R. Živaljević |
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Аннотация:
The general Tverberg–Van Kampen–Flores problem is to find higher dimensional analogues of results about non-planarity of graphs. More precisely, the problem is to find interesting examples of simplicial complexes which are $r$-non-embeddable in $\mathbb{R}^d$ in the sense that they cannot be mapped to $\mathbb{R}^d$ without $r$-fold points.
For illustration, the graphs $K_{3,3}$ and $K_5$ are $2$-non-embeddable in
$\mathbb{R}^2$ while the $2$-dimensional complex $K_{5,5,5} = [5]*[5]*[5]$ is $3$-non-embeddable in $\mathbb{R}^3$. Extending the results of Grünbaum, Sarkaria, Schild,
Blagojević, Frick, Ziegler, and many others, we show that interesting examples of $r$-non-embeddable complexes can be found among the joins $K = K_1*\ldots* K_s$ of so called $r$-unavoidable complexes.
Язык доклада: английский
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