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Lobachevskii Journal of Mathematics, 2006, Volume 22, Pages 35–46
(Mi ljm43)
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This article is cited in 4 scientific papers (total in 4 papers)
Index vector-function and minimal cycles
A. V. Lapteva, E. I. Yakovlev N. I. Lobachevski State University of Nizhni Novgorod
Abstract:
Let $P$ be a closed triangulated manifold, $\dim{P}=n$. We consider the group of simplicial 1-chains $C_1(P)=C_1(P,\mathbb Z_2)$ and the homology group $H_1(P)=H_1(P,\mathbb Z_2)$. We also use some nonnegative weighting function $L\colon C_1(P)\to\mathbb R$. For any homological class $[x]\in H_1(P)$ the method proposed in article builds a cycle $z\in[x]$ with minimal weight $L(z)$. The main idea is in using a simplicial scheme of space of the regular covering $p\colon\hat P\to P$ with automorphism group $G\cong H_1(P)$. We construct this covering applying the index vector-function $J\colon C_1(P)\to\mathbb Z_2^r$ relative to any basis of group $H_{n-1}(P)$, $r=\operatorname{rank}H_{n-1}(P)$.
Keywords:
triangulated manifold, homology group, minimal cycle, intersection index, regular covering.
Citation:
A. V. Lapteva, E. I. Yakovlev, “Index vector-function and minimal cycles”, Lobachevskii J. Math., 22 (2006), 35–46
Linking options:
https://www.mathnet.ru/eng/ljm43 https://www.mathnet.ru/eng/ljm/v22/p35
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Abstract page: | 258 | Full-text PDF : | 81 | References: | 48 |
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