Corpus ID: 207852945

Spherical complexities, with applications to closed geodesics.

@article{Mescher2019SphericalCW,
  title={Spherical complexities, with applications to closed geodesics.},
  author={Stephan Mescher},
  journal={arXiv: Geometric Topology},
  year={2019}
}
  • Stephan Mescher
  • Published 2019
  • Mathematics
  • arXiv: Geometric Topology
  • 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… CONTINUE READING

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