A Boothby–Wang Theorem for Besse Contact Manifolds
| Autor: | Christian Lange, Marc Kegel |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
General Mathematics Computer Science::Digital Libraries 01 natural sciences Perspective (geometry) Besse contact manifolds 0103 physical sciences Symplectic orbifold 0101 mathematics ddc:510 Mathematics::Symplectic Geometry Orbifold Quotient Mathematics 010102 general mathematics Periodic Reeb flow Lie group 510 Mathematik Orbibundles Manifold Boothby–Wang theorem Flow (mathematics) Computer Science::Mathematical Software Equivariant map Mathematics::Differential Geometry 010307 mathematical physics Symplectic geometry |
| DOI: | 10.18452/26661 |
| Popis: | A Reeb flow on a contact manifold is called Besse if all its orbits are periodic, possibly with different periods. We characterize contact manifolds whose Reeb flows are Besse as principal $$S^1$$ S 1 -orbibundles over integral symplectic orbifolds satisfying some cohomological condition. Apart from the cohomological condition, this statement appears in the work of Boyer and Galicki in the language of Sasakian geometry (Boyer and Galicki in Sasakian geometry, Oxford Mathematical Monographs, Oxford University Press, Oxford, 2008). We illustrate some non-commonly dealt with perspective on orbifolds in a proof of the above result. More precisely, we work with orbifolds as quotients of manifolds by smooth Lie group actions with finite stabilizer groups. By introducing all relevant orbifold notions in this equivariant way, we avoid patching constructions with orbifold charts. As an application, and building on work by Cristofaro-Gardiner–Mazzucchelli, we deduce a complete classification of closed Besse contact 3-manifolds up to strict contactomorphism. |
| Databáze: | OpenAIRE |
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