Two-dimensional measured laminations of positive Euler characteristic (Q2730926)
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scientific article; zbMATH DE number 1625250
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two-dimensional measured laminations of positive Euler characteristic |
scientific article; zbMATH DE number 1625250 |
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19 June 2002
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measured lamination
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branched surface
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sphere lemma
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Two-dimensional measured laminations of positive Euler characteristic (English)
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A new proof of Connes's Sphere Lemma that a compact oriented, 2-dimensional measured lamination \(\Lambda\) of positive Euler characteristic, \(\chi(\Lambda) > 0\), has at least one leaf homeomorphic to the 2-sphere, is presented. In fact, the total transverse measure of the 2-sphere leaves is at least \(\chi(\Lambda)/2\). The new proof uses branched surface methods and some measure theory by way of Rokhlin's Lemma applied to the holonomy map. For the original proof, see [\textit{A. Connes}, Noncommutative geometry (1994; Zbl 0818.46076)].
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