Computing v1 -periodic homotopy groups of spheres and some compact Lie groups Donald M. Davis Contents 1.Introduction 2.Definition of v1-periodic homotopy groups 3.The isomorphism v11ss (S2n+1) ss v11sss2n1 (Bqn) 4.J-homology 5.The v1-periodic homotopy groups of spectra 6.The v1-periodic UNSS for spheres 7.v1-periodic homotopy groups of SU(n) 8.v1-periodic homotopy groups of some Lie groups References HANDBOOK OF ALGEBRAIC TOPOLOGY Edited by I.M. James 1995 Elsevier Science B.V. All rights reserved