I need the english translation of the article (or book) by jean-Pierre Serre in French on the topic Homologie singulière des espaces fibrés
I am interested in understanding about this conjecture: there exist infinitely many geodesics between two points on a closed Riemannian manifold. Does there exist a translation?

Links to the French original:

On JSTOR http://www.jstor.org/discover/10.2307/1969485?uid=3738016&uid=2129&uid=2&uid=70&uid=4&sid=21102499009897

or see also http://www.maths.ed.ac.uk/~aar/papers/serre.pdf

Related post: Translations of Serre's early spectral sequences papers


closed as unclear what you're asking by Mark Sapir, alvarezpaiva, Loop Space, Did, Yemon Choi Jul 1 '13 at 8:25

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  • $\begingroup$ possible duplicate of Translations of Serre's early spectral sequences papers $\endgroup$ – Did Jul 1 '13 at 8:08
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    $\begingroup$ To close this because it would be "unclear what you're asking" strikes me as rather odd. $\endgroup$ – Did Jul 1 '13 at 8:12
  • $\begingroup$ How about the manifold $S^1$? I think you may need to consider your intended question more carefully $\endgroup$ – Yemon Choi Jul 1 '13 at 8:27
  • $\begingroup$ I voted to close because this question does not show adequate care or forethought before asking it, see meta.mathoverflow.net/questions/203 $\endgroup$ – Yemon Choi Jul 1 '13 at 8:35
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    $\begingroup$ $S^1$ is fine: take the segment between the points and concatenate with multiples of the closed geodesic. This is a problem of critical points in the loop space, so going around many times is allowed. $\endgroup$ – alvarezpaiva Jul 1 '13 at 8:39

this is Serre's Ph.D. thesis; it has been translated into english but only the introduction is available for free:


the remaining 100 pages are behind a £ 20 paywall:



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