Geodesic
Self homotopy equivalences of classifying spaces of compact connected Lie groups
Fundamenta Mathematicae, Tome 147 (1995) no. 2, pp. 99-126.

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We describe, for any compact connected Lie group G and any prime p, the monoid of self maps $BG_{^p}$ → $BG_{^p}$ which are rational equivalences. Here, $BG_{^p}$ denotes the p-adic completion of the classifying space of G. Among other things, we show that two such maps are homotopic if and only if they induce the same homomorphism in rational cohomology, if and only if their restrictions to the classifying space of the maximal torus of G are homotopic.
DOI : 10.4064/fm-147-2-99-126

Stefan Jackowski 1 ; James McClure 1 ; Bob Oliver 1

1 
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Stefan Jackowski; James McClure; Bob Oliver. Self homotopy equivalences of classifying spaces of compact connected Lie groups. Fundamenta Mathematicae, Tome 147 (1995) no. 2, pp. 99-126. doi : 10.4064/fm-147-2-99-126. http://geodesic.mathdoc.fr/articles/10.4064/fm-147-2-99-126/

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