Abstract
AbstractWe provide an effective estimate on the Betti numbers of the loop space of a compact manifold which admits a finite Grauert tube. It implies the polynomial estimate in Chen (arXiv:2101.04368, 2021) after taking the radius of the tube to infinity.
Publisher
Springer Science and Business Media LLC
Reference13 articles.
1. Besse, A.: Manifolds All of Whose Geodesics are Closed. A series of Modern Surveys in Mathematics, vol. 93. Springer, Berlin (1978)
2. Burns, D.: Curvature of Monge-Amèpe foliations and parabolic manifolds. Ann. Math. 115, 349–373 (1982)
3. Chen, X.: Riemannian manifolds with entire Grauert tube are rationally elliptic (2021). arXiv: 2101.04368
4. Evans, L., Gariepy, R.: Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics, CRC Press, Boca Raton (1992)
5. Grauert, H.: On Levi’s problem and the imbedding of real analytic manifolds. Ann. Math. 68, 460–472 (1958)