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Семинар международной лаборатории алгебраической топологии и ее приложений (АТиП)
13 мая 2021 г. 18:10–19:40, г. Москва, Покровский бульвар, 11, ауд. R408. Необходимо заказать пропуск у менеджера лаборатории. Zoom: https://us02web.zoom.us/j/83690225045?pwd=WkFNSUlubUVzL3NpZXlMZU45Wk9vdz09 Пароль необходимо запросить у менеджера лаборатории.
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[A Higher-Dimensional Generalization of the Heawood Theorem on Embeddings of Graphs into Surfaces]
Е. С. Коган, А. Б. Скопенков |
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Аннотация:
We present a short well-structured exposition of the 2019 Patak-Tancer higher-dimensional generalization of the Heawood inequality for embeddings of graphs into surfaces. This exposition clarifies the relation of the Patak-Tancer proof to earlier known results. This exposition is accessible to non-specialists in the field.
A simplified version of the Patak-Tancer result is as follows.
Theorem. If the union of k-dimensional faces of the n-dimensional simplex PL embeds into the connected sum of g copies of the Cartesian product S^k \times S^k of two k-dimensional spheres, then g is at least (n-2k-1)/(k+2).
Язык доклада: английский
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