Contractible space of maps between Eilenberg-Mac Lane spaces, 2 - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T21:14:21Z http://mathoverflow.net/feeds/question/53116 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/53116/contractible-space-of-maps-between-eilenberg-mac-lane-spaces-2 Contractible space of maps between Eilenberg-Mac Lane spaces, 2 Jeff Strom 2011-01-24T20:06:38Z 2011-01-24T20:36:22Z <p>Let $G$ and $H$ be torsion abelian groups. Are the following are equivalent:</p> <ol> <li><p>$\mathrm{Hom}(G, H) = 0$</p></li> <li><p>$\mathrm{map}_*( K(G, m), K(H,n)) \sim *$ for all $n, m\geq 1$</p></li> </ol> <p>?</p> <p>Clearly (2) implies (1).</p> http://mathoverflow.net/questions/53116/contractible-space-of-maps-between-eilenberg-mac-lane-spaces-2/53118#53118 Answer by Neil Strickland for Contractible space of maps between Eilenberg-Mac Lane spaces, 2 Neil Strickland 2011-01-24T20:24:26Z 2011-01-24T20:24:26Z <p>No, we have $Hom(\mathbb{Z}/n,\mathbb{Z})=0$ but there is a nontrivial Bockstein $K(\mathbb{Z}/n,1)\to K(\mathbb{Z},2)$.</p> <p>For finite abelian groups we have (1) iff (2) iff ($|G|$ and $|H|$ are coprime).</p>