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

Yuming Xiao; Yiming Long

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arXiv · 1503.07006

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

Yuming Xiao·Yiming Long

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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.

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Yuming Xiao, Yiming Long. 2015-03-24. Topological structure of non-contractible loop space and closed geodesics on real projective spaces with odd dimensions. https://arxiv.org/abs/1503.07006

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