# English translation of book by Jean-Pierre Serre? [closed]

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:

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

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

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question.

possible duplicate of Translations of Serre's early spectral sequences papers – Did Jul 1 '13 at 8:08
To close this because it would be "unclear what you're asking" strikes me as rather odd. – Did Jul 1 '13 at 8:12
How about the manifold $S^1$? I think you may need to consider your intended question more carefully – Yemon Choi Jul 1 '13 at 8:27
I voted to close because this question does not show adequate care or forethought before asking it, see meta.mathoverflow.net/questions/203 – Yemon Choi Jul 1 '13 at 8:35
$S^1$ 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. – alvarezpaiva Jul 1 '13 at 8:39

## 1 Answer

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

http://www.worldscientific.com/doi/suppl/10.1142/8444/suppl_file/8444_chap01.pdf

the remaining 100 pages are behind a £ 20 paywall:

http://www.worldscientific.com/doi/pdf/10.1142/9789814401319_0001

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thanks a lot!it was very useful. – azita lekpour Jul 10 '13 at 13:58