The p-equivalence of \(SO(2n+1)\) and Sp(n)
It is shown how one can obtain a map to establish that when \(SO(2n+1)\) and Sp(n) are localized at the set of odd primes, then they are homotopy equivalent, in fact H-equivalent. It is not known if this map is a loop map. The author assumes the work of Harris establishing the corresponding result for homotopy groups but not Friedlander's results on localized classifying spaces. The ingredients are explicit homotopy theory and work of the author in the 1960's.
homotopy equivalences of localized spaces
scientific article; zbMATH DE number 3872259