TORSION IN THE SPACE OF COMMUTING ELEMENTS IN A LIE GROUP (New trends of transformation groups)

Abstract

Let G be a compact connected Lie group, and let Hom (ℤ[m]，G) denote the space of homomorphisms from a free abelian group ℤ[m] to G. We study the problem of which primes p Hom (ℤ[m]，G) has p-torsion in homology. We give a new homotopy decomposition of the space, and we prove that Hom(ℤ[m], SU(n)) for m ≥ 2 hasp-torsion in homology if and only if p ≤ n. In this text we overview the proof and observe some examples.