Types of fixed points of index one of surface homeomorphisms (Q2748987)
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scientific article; zbMATH DE number 1663596
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Types of fixed points of index one of surface homeomorphisms |
scientific article; zbMATH DE number 1663596 |
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Types of fixed points of index one of surface homeomorphisms (English)
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7 July 2002
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fixed points
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area-preserving maps
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index theory
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Let \(f\) be an area and orientation preserving homeomorphism of a surface, and \(p\) be its isolated fixed point of index \(1\). Consider a small disk neighborhood \(D\) of \(p\). For a lift of \(f\) to the universal cover of \(D\setminus\{p\}\) the author defines its type, which is either positive or negative. This concept is used to prove a fixed point theorem. Moreover, a refinement of the Arnold conjecture about the number of fixed points of a surface homeomorphism is obtained.
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