We prove existence theorems representing homotopy classes by p-harmonic maps of least p-energy, and representing nthhomotopy classes by n-harmonic maps, generalizing theorems of Cartan and ...

K-Theory and homotopy theory constitute pivotal branches of modern mathematics, forming a bridge between algebraic invariants and topological structures. This intersection has fostered the development ...

Let EΩ(X) be the group of homotopy classes of self-homotopy equivalences of X such that Ω f ≃ 1dΩ X. We prove that EΩ(X) is a nilpotent group and that nil EΩ(X) ≤ cat(X) - 1.