English

Topological structure of non-contractible loop space and closed geodesics on real projective spaces with odd dimensions

Geometric Topology 2015-03-25 v1

Abstract

In this paper, we use Chas-Sullivan theory on loop homology and Leray-Serre spectral sequence to investigate the topological structure of the non-contractible component of the free loop space on the real projective spaces with odd dimensions. Then we apply the result to get the resonance identity of non-contractible homologically visible prime closed geodesics on such spaces provided the total number of distinct prime closed geodesics is finite.

Keywords

Cite

@article{arxiv.1503.07006,
  title  = {Topological structure of non-contractible loop space and closed geodesics on real projective spaces with odd dimensions},
  author = {Yuming Xiao and Yiming Long},
  journal= {arXiv preprint arXiv:1503.07006},
  year   = {2015}
}

Comments

43 pages, 1 figure