Samelson products and exponents of homotopy groups

Abstract

This paper is an introduction to homotopy groups with coefficients, their Samelson products, and their main applications to higher order torsion in the homotopy groups of Moore spaces and to exponents of the homotopy groups of spheres. All this material is treated in the author’s book (Neisendorfer in Algebraic methods in unstable homotopy theory, Cambridge University Press, 2009). Other useful references are the author’s memoir, Primary homotopy theory (Neisendorfer in Mem AMS 232, American Mathematical Society, 1980), and the author’s paper, Homotopy groups with coefficients (Neisendorfer in J Fixed Point Theory Appl 8:247–338, 2010).