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2021 Spherical complexities with applications to closed geodesics
Stephan Mescher
Algebr. Geom. Topol. 21(2): 1021-1074 (2021). DOI: 10.2140/agt.2021.21.1021

Abstract

We construct and discuss new numerical homotopy invariants of topological spaces that are suitable for the study of functions on loop and sphere spaces. These invariants resemble the Lusternik–Schnirelmann category and provide lower bounds for the numbers of critical orbits of SO(n)–invariant functions on spaces of n–spheres in a manifold. Lower bounds on these invariants are derived using weights of cohomology classes. As an application, we prove new existence results for closed geodesics on Finsler manifolds of positive flag curvature satisfying a pinching condition.

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Stephan Mescher. "Spherical complexities with applications to closed geodesics." Algebr. Geom. Topol. 21 (2) 1021 - 1074, 2021. https://doi.org/10.2140/agt.2021.21.1021

Information

Received: 8 December 2019; Revised: 28 April 2020; Accepted: 15 June 2020; Published: 2021
First available in Project Euclid: 28 May 2021

Digital Object Identifier: 10.2140/agt.2021.21.1021

Subjects:
Primary: 55S40, 58E05
Secondary: 58E10

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.21 • No. 2 • 2021
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