Subject: RE: four postings From: "Ron Umble" Date: Mon, 19 Feb 2007 11:34:47 -0500 Jim, In his talk at the Lehigh conference last summer, Ralph Cohen discussed the case [S,X] where S is a surface of genus g and X a 1-connected mfld. You might want to check with him. He can probably point you in the right direction. Ron Subject: question for all From: jim stasheff Date: Sat, 17 Feb 2007 16:04:33 -0500 I have a dim memory of someone's paper on homotopy classes of maps FROM a torus I have in mind the unstable range (S1)^n \to S2 with n > 2 so do not have the usual cohomotopy *group* structure anyone have a similar memory? jim _____________________________________________________________ Subject: Re: four postings From: "Ronnie Brown" Date: Mon, 19 Feb 2007 17:24:59 -0000 Jim, Maybe you are thinking of a paper by RHFox `Torus homotopy groups' Annals of Math. I was told by Brian Griffiths that Fox was really thinking of things like Higher Homotopy van Kampen theorems (adding relations to homotopy groups) but he dod not achieve this. He was still thinking in terms of groups, whereas you all know my view that you have to use groupoids and higher groupoids to get good local-to-global theorems, since in the cubical type situation you can get algebraic inverses to subdivision. That was the basic intuition pursued since 1966. I also wondered why Frank Adam's arguments for the cellular appproximation theorem (subdivision, and reproduced in my book) did not produce algebraic results, as did the analogous 1-dimensional case. There seemed to be a lack of an appropriate algebraic gadget. It took only 11 years to produce it, fortunately collaborating with Chris Spencer, and then Philip Higgins. I have put a number of papers as pdf files from http://www.bangor.ac.uk/~mas010/publicfull.htm They need some reorganisation into themes, perhaps. Will do in time. Ronnie Brown