Geodesic
On the cohomology of loop spaces of compact Lie groups
Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 91-99

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a compact, simply-connected Lie group. The cohomology of the loop space ΏG has been described by Bott, both in terms of a cell decomposition [1] and certain homogeneous spaces called generating varieties [2]. It is possible to view ΏG as an infinite dimensional “Grassmannian” associated to an appropriate infinite dimensional group, cf. [3], [7]. From this point of view the above cell-decomposition of Bott arises from a Bruhat decomposition of the associated group. We choose a generator H ∈ H2(ΏG, Z) and call it the hyperplane class. For a finite-dimensional Grassmannian the highest power of H carries geometric information about the variety, namely, its degree. An analogous question for ΏG is: What is the largest integer Nk = Nk(G) which divides Hk ∈ H2k(ΏG, Z)?Of course, if G = SU(2) = S3, one knows Nk = h!. In general, the deviation of Nk from k! measures the failure of H to generate a divided polynomial algebra in H*(ΏG, Z). 
Hiller, Howard. On the cohomology of loop spaces of compact Lie groups. Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 91-99. doi: 10.1017/S0017089500005814
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