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Mathematische Zeitschrift

, Volume 244, Issue 1, pp 1–34 | Cite as

Commutative free loop space models at large primes

  • N. Dupont
  • K. Hess

Abstract.

Let p be a prime number and \(\) a natural number. If E is a r-connected finite CW-complex of dimension at most pr, then E is an example of a p-Anick space. For p > 2 we construct a commutative cochain algebra over \(\) that is an \(\)-model of the free loop space on a p-Anick space, i.e., its cohomology algebra is isomorphic to the mod p cohomology of the free loop space. For p-Anick spaces that are p-formal, such as spheres and projective spaces, we define an even simpler commutative free loop space model that applies for all primes p. We then use the simplified model to compute the cohomology algebras of a number of free loop spaces explicitly.

Keywords

Natural Number Projective Space Prime Number Space Model Loop Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • N. Dupont
    • 1
  • K. Hess
    • 2
  1. 1.UFR de mathématiques, Université de Lille I, F-59655 Villeneuve d'Ascq, France (e-mail: Nicolas.Dupont@univ-lille1.fr) FR
  2. 2. Département de mathématiques, EPFL, CH-1015 Lausanne, Switzerland (e-mail: kathryn.hess@epfl.ch) CH

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