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Funktsional'nyi Analiz i ego Prilozheniya, 2024, Volume 58, Issue 1, Pages 22–41
DOI: https://doi.org/10.4213/faa4193
(Mi faa4193)
 

This article is cited in 1 scientific paper (total in 1 paper)

Polynomial Eulerian characteristic of nilmanifolds

V. M. Buchstaber

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
References:
Abstract: The article studies bundle towers $M^{n+1}\to M^{n}\to \dots \to S^1$, $\geqslant 1$, with fiber $S^1$, where $M^n = L^n\!/\Gamma^n$ are compact smooth nilmanifolds and $L^n\thickapprox \mathbb{R}^n$ is a group of polynomial transformations of the line $\mathbb{R}^1$. The focus is on the well-known problem of calculating cohomology rings with rational coefficients of manifolds $M^n$. Using the canonical bigradation in the de Rham complex of manifolds $M^n$, we introduce the concept of polynomial Eulerian characteristic and calculate it for these manifolds.
Keywords: bigraded de Rham complex, polynomial transformations of a line, algebra of left invariant differential operators, Gysin exact sequence.
Received: 02.01.2024
Revised: 02.01.2024
Accepted: 05.01.2024
English version:
Functional Analysis and Its Applications, 2024, Volume 58, Issue 1, Pages 16–32
DOI: https://doi.org/10.1134/S0016266324010039
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. M. Buchstaber, “Polynomial Eulerian characteristic of nilmanifolds”, Funktsional. Anal. i Prilozhen., 58:1 (2024), 22–41; Funct. Anal. Appl., 58:1 (2024), 16–32
Citation in format AMSBIB
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\paper Polynomial Eulerian characteristic of nilmanifolds
\jour Funktsional. Anal. i Prilozhen.
\yr 2024
\vol 58
\issue 1
\pages 22--41
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\jour Funct. Anal. Appl.
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\vol 58
\issue 1
\pages 16--32
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Linking options:
  • https://www.mathnet.ru/eng/faa4193
  • https://doi.org/10.4213/faa4193
  • https://www.mathnet.ru/eng/faa/v58/i1/p22
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
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    Abstract page:281
    Full-text PDF :15
    Russian version HTML:24
    References:43
    First page:40
     
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