Abstract
AbstractA 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.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Reference48 articles.
1. Abbondandolo, A., Bramham, B., Hryniewicz, U.L., Salomão, P.A.S.: A systolic inequality for geodesic flows on the two-sphere. Math. Ann. 367(1–2), 701–753 (2017)
2. Abbondandolo, A., Bramham, B., Hryniewicz, U.L., Salomão, P.A.S.: Sharp systolic inequalities for Reeb flows on the three-sphere. Invent. Math. 211(2), 687–778 (2018)
3. Abbondandolo, A., Benedetti, G.: On the local systolic optimality of Zoll contact forms (2019). arXiv:1912.04187, preprint
4. Adem, A., Leida, J., Ruan, Y.: Orbifolds and Stringy Topology. Cambridge Tracts in Mathematics, vol. 171. Cambridge University Press, Cambridge (2007)
5. Agol, I.: Ring structure on group cohomology. https://mathoverflow.net/questions/133974/, visited on ((2020)-03-19)
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献