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Fundamental group and contractible closed geodesics

✍ Scribed by Alexander Nabutovsky

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
813 KB
Volume
49
Category
Article
ISSN
0010-3640

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✦ Synopsis

We prove the existence of a nonempty class of finitely presented groups with the following property: If the fundamental group of a compact Riemannian manifold M belongs to this class, then there exists a constant c ( M ) > 1 such that for any sufficiently large 5 the number of contractible closed geodesics on A4 of length not exceeding 2 is greater than c(M)".

In order to prove this result, we give a lower bound for the number of contractible closed geodesics of length 5 2 on a compact Riemannian manifold M in terms of the resourcebounded Kolmogorov complexity of the word problem for ~1 (M), thus answering a question posed by Gromov. @

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