Многогранники, Числа Фибоначчи, Алгебры Хопфа И Квазисимметрические Функции

Бухштабер, Виктор Матвеевич; Buchstaber, Victor Matveevich; Ероховец, Николай Юрьевич; Erokhovets, Nikolai Yur'evich

doi:10.4213/rm9421

Uspekhi Mat. Nauk

2011

DOI: 10.4213/rm9421

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Многогранники, Числа Фибоначчи, Алгебры Хопфа И Квазисимметрические Функции

Виктор Матвеевич Бухштабер¹,

Victor Matveevich Buchstaber²,

Николай Юрьевич Ероховец³

et al.

Abstract: Обзор посвящен классической проблеме флаговых чисел выпуклых многогранников. Излагаются результаты, полученные на основе связи теории выпуклых многогранников с рядом современных направлений исследований. Библиография: 62 названия.

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Cited by 10 publications

References 52 publications

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Massey products, toric topology and combinatorics of polytopes

Buchstaber¹,

Limonchenko²

2019

Izv. Math.

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In this paper we introduce a direct family of simple polytopes such that for any there are non-trivial strictly defined Massey products of order in the cohomology rings of their moment-angle manifolds . We prove that the direct sequence of manifolds has the following properties: every manifold is a retract of , and one has inverse sequences in cohomology (over and , where as ) of the Massey products constructed. As an application we get that there are non-trivial differentials , for arbitrarily large as , in the Eilenberg–Moore spectral sequence connecting the rings and with coefficients in a field, where .

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Massey products, toric topology and combinatorics of polytopes

Buchstaber¹,

Limonchenko²

2019

Izv. Math.

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Viktor Matveevich Buchstaber (on his 70th birthday)

Вершик¹,

Веселов²,

Gaifullin³

et al. 2013

Russ. Math. Surv.

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Virtual polytopes

Panina¹,

Streinu²

2015

Russ. Math. Surv.

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Многогранники, Числа Фибоначчи, Алгебры Хопфа И Квазисимметрические Функции

Cited by 10 publications

References 52 publications

Massey products, toric topology and combinatorics of polytopes

Massey products, toric topology and combinatorics of polytopes

Viktor Matveevich Buchstaber (on his 70th birthday)

Virtual polytopes

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