Subject: Re: question about framed bordism From: "Dr A. J. Baker" Date: Thu, 15 Mar 2007 15:00:12 -0000 (GMT) Dear Johannes, For principal coverings with fibre a finite group, G say,this is really about the transfer \pi^S_nBG_+ -> \pi^S_nEG_+ = \pi^S_n and this was studied quite a bit for symmetric groups, and cyclic groups (and more generally the circle). You might look at the reviews MR0418091 MR0377873 MR0309109 and other sources I can't think of offhand. More locally look at K. Knapp, Some application of ${\rm K}$-theory to framed bordism; $e$-invariant and transfer, Habilitationsschrift, Bonn, 1979. Hope that helps, Andy >> Subject: A question for the topology list >> From: Johannes Ebert >> Date: Wed, 14 Mar 2007 14:04:55 +0100 (CET) >> >> here is a question for the toplogy list. You all know that the n th stable >> homotopy group of spheres is framed bordism of framed n-manifolds. Now I >> consider a closed n- manifold M and a framing a of M. Let f:N \to M be a >> finite covering. This induces a framing f^*a of N. Here is the question: >> >> Is there any general statement which relates the elements [M,a] and >> [N,f^*a] in the stable homotopy group? >> >> Best, >> Johannes >> Dr A. J. Baker Department of Mathematics University of Glasgow Glasgow G12 8QW Scotland phone (0141) 330 6140 fax (0141) 330 4111 a.baker@maths.gla.ac.uk http://www.maths.gla.ac.uk/~ajb/