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Zapiski Nauchnykh Seminarov POMI, 2008, Volume 353, Pages 181–190
(Mi znsl1642)
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This article is cited in 1 scientific paper (total in 1 paper)
Order of a function on the Bruschlinsky group of a two-dimensional polyhedron
S. S. Podkorytov St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
Homotopy classes of mappings of a compact polyhedron $X$ to the circle $T$ form an Abelian group $B(X)$, which is called the Bruschlinsky group and is isomorphic to $H^1(X;\mathbb Z)$. A function $f\colon B(X)\to L$, where $L$ is an Abelian group, has order at most $r$ if for each mapping $a\colon X\to T$ the value $f([a])$ is $\mathbb Z$-linearly expressed via the characteristic function $I_r(a)\colon(X\times T)^r\to\mathbb Z$ of $(\Gamma_a)^r$, where $\Gamma_a\subset X\times T$ is the graph of $a$. The function $f$ has degree at most $r$ if the finite differences of $f$ of order $r+1$ vanish. Conjecturally, the order of $f$ equals the algebraic degree of $f$. The conjecture is proved in the case where $\dim X\le2$. Bibl. – 1 title.
Received: 16.02.2007
Citation:
S. S. Podkorytov, “Order of a function on the Bruschlinsky group of a two-dimensional polyhedron”, Geometry and topology. Part 10, Zap. Nauchn. Sem. POMI, 353, POMI, St. Petersburg, 2008, 181–190; J. Math. Sci. (N. Y.), 161:3 (2009), 454–459
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https://www.mathnet.ru/eng/znsl1642 https://www.mathnet.ru/eng/znsl/v353/p181
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Abstract page: | 192 | Full-text PDF : | 52 | References: | 28 |
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