An equivariant CW-complex for the free loop space of a Finsler manifold (Q2888971)
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scientific article; zbMATH DE number 6042781
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An equivariant CW-complex for the free loop space of a Finsler manifold |
scientific article; zbMATH DE number 6042781 |
Statements
4 June 2012
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closed geodesics
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geodesic polygons
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free loop space
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equivariant CW-complex
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equivariant homotopy type
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0.8867253
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0.8837986
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0.88351905
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0.8816439
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0.88039315
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0.8777893
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0.8774263
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An equivariant CW-complex for the free loop space of a Finsler manifold (English)
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For a compact manifold \(M\) endowed with a bumpy Finsler metric, the author considers the free loop space of absolutely continuous closed curves \(\gamma:S^1{\rightarrow}M\) with finite energy and the canonical action of the group \(S^1\) on it. Using Morse theory for the energy functional, the author constructs with the help of a space of geodesic polygons an equivariant \(CW\) complex which is \(S^1\)-homotopy equivalent to the free loop space.NEWLINENEWLINEFor the entire collection see [Zbl 1237.58002].
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