Regular geometric cycles (Q2795674)
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scientific article; zbMATH DE number 6559192
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Regular geometric cycles |
scientific article; zbMATH DE number 6559192 |
Statements
22 March 2016
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geometric cycle
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systol
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systolic volume
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Eilenberg-McLane space
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cubical complex
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math.GT
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math.AT
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math.MG
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Regular geometric cycles (English)
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Let \(\pi\) be a finitely presented group. If \(h\) is a non-trivial homology class in \(H_n(\pi ;\mathbb Z)\), a theorem of \textit{M. Gromov} [J. Differ. Geom. 18, 1--147 (1983; Zbl 0515.53037)] asserts the existence of regular geometric cycles which represent \(h\), whose relative systolic volume is as close as desired to the systolic volume of \(h\), in which we can control the volume of balls of radius less than half of the cycle's relative systol. The author explains and provides a complete proof of this result.
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