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Симплициальный объём — топологический инвариант, определённый для замкнутых многообразий. Впервые рассмотрен Громовым.Симплициальный объём многообразия обычно обозначается .
, In the mathematical field of geometric top … In the mathematical field of geometric topology, the simplicial volume (also called Gromov norm) is a certain measure of the topological complexity of a manifold. More generally, the simplicial norm measures the complexity of homology classes. Given a closed and oriented manifold, one defines the simplicial norm by minimizing the sum of the absolute values of the coefficients over all singular chains representing a cycle. The simplicial volume is the simplicial norm of the fundamental class. It is named after Mikhail Gromov, who introduced it in 1982. With William Thurston, he proved that the simplicial volume of a finite volume hyperbolic manifold is proportional to the hyperbolic volume. The simplicial volume is equal to twice the Thurston norm Thurston also used the simplicial volume to prove that hyperbolic volume decreases under hyperbolic Dehn surgery.e decreases under hyperbolic Dehn surgery.
, In der Mathematik ist simpliziales Volumen … In der Mathematik ist simpliziales Volumen eine Homotopieinvariante geschlossener Mannigfaltigkeiten, die von Gromow in seinem Beweis der Mostow-Starrheit eingeführt wurde. Intuitiv misst das simpliziale Volumen, wie schwierig es ist, die Mannigfaltigkeit durch Simplizes (mit reellen Koeffizienten) darzustellen. (mit reellen Koeffizienten) darzustellen.
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| rdfs:comment |
In the mathematical field of geometric top … In the mathematical field of geometric topology, the simplicial volume (also called Gromov norm) is a certain measure of the topological complexity of a manifold. More generally, the simplicial norm measures the complexity of homology classes. Given a closed and oriented manifold, one defines the simplicial norm by minimizing the sum of the absolute values of the coefficients over all singular chains representing a cycle. The simplicial volume is the simplicial norm of the fundamental class. The simplicial volume is equal to twice the Thurston normvolume is equal to twice the Thurston norm
, In der Mathematik ist simpliziales Volumen … In der Mathematik ist simpliziales Volumen eine Homotopieinvariante geschlossener Mannigfaltigkeiten, die von Gromow in seinem Beweis der Mostow-Starrheit eingeführt wurde. Intuitiv misst das simpliziale Volumen, wie schwierig es ist, die Mannigfaltigkeit durch Simplizes (mit reellen Koeffizienten) darzustellen. (mit reellen Koeffizienten) darzustellen.
, Симплициальный объём — топологический инвариант, определённый для замкнутых многообразий. Впервые рассмотрен Громовым.Симплициальный объём многообразия обычно обозначается .
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Simplicial volume
, Симплициальный объём
, Simpliziales Volumen
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