Volume entropy semi-norm and systolic volume semi-norm (Q6620338)
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scientific article; zbMATH DE number 7927736
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Volume entropy semi-norm and systolic volume semi-norm |
scientific article; zbMATH DE number 7927736 |
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Volume entropy semi-norm and systolic volume semi-norm (English)
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16 October 2024
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This paper introduces two new semi-norms on the real homology of a path-connected topological space, the volume entropy semi-norm, which is related to the notion of volume entropy, and the systolic volume semi-norm, which is related to an asymptotic optimal inequality in systolic geometry. These two semi-norms satisfy the functorial properties of the semi-norm that \textit{M. Gromov} [Publ. Math., Inst. Hautes Étud. Sci. 56, 5--99 (1982; Zbl 0516.53046)] used for the definition of the simplicial volume. In fact, as semi-norms, they are both equivalent to the Gromov semi-norm.
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simplicial volume
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volume entropy
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systolic volume
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functorial geometric semi-norms
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