The Bott–Samelson theorem for positive Legendrian isotopies
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The classical Bott–Samelson theorem states that if on a Riemannian manifold all geodesics issuing from a certain point return to this point, then the universal cover of the manifold has the cohomology ring of a compact rank one symmetric space. This result on geodesic flows has been generalized to Reeb flows and partially to positive Legendrian isotopies by Frauenfelder–Labrousse–Schlenk. We prove the full theorem for positive Legendrian isotopies.
KeywordsBott–Samelson theorem Positive Legendrian loop Slow entropy
Mathematics Subject ClassificationPrimary 53D35 Secondary 53D40 57R17
I wish to thank Felix Schlenk and the anonymous referee for their valuable suggestions. This work is supported by SNF Grant 200021-163419/1.