Two responses to yesterday's question. (It may look different than usual; I just got a new computer, and am learning how to use it.)...DMD __________________________________________________________________ Subject: Re: two questions From: "Dev P. Sinha" Date: Thu, 12 Aug 2004 08:23:17 -0700 I think that some of Chen's work addresses such questions. My suggestion is to look at his collected works, since such results are contained in different papers (and I can't specify one off the top of my head). On Aug 12, 2004, at 5:02 AM, Don Davis wrote: > Two postings, both questions..........DMD > _________________________________________________________ > > Subject: Question for Topology Discussion List > Date: Wed, 11 Aug 2004 11:13:33 +0100 > From: Martin Crossley > > One of my colleagues has a question that he asked me to put to the list: > >> I vaguely remember something written on finding out information >> on the fundamental group (or higher homotopy groups?) of a manifold >> from the de Rham complex - information additional to the non-torsion >> part of the abelianisation that is, so not just deducible from the >> cohomology. If anyone could give me a clue where to look I would be >> grateful. >> > > Thanks, > Martin Crossley _____________________________________________________________________ Subject: Re: two questions From: "Simon Willerton" Date: Thu, 12 Aug 2004 20:21:46 +0100 The first place that pops to mind is Chapter 5 of my thesis, which I can make available as that part was never published -- I was interested in K(G,1)s so didn't do anything on higher homotopy groups. I guess the obvious places to look would be a couple of papers of Sullivan's such as ["Differential forms and the topology of manifolds" Manifolds Tokyo 1973], or ["Infinitesimal computations in topology" IHES Publ. Math. 47 (1977)] (but I haven't looked at either myself for ages, so I can't really remember what's in them). As far as I recall, books on rational homotopy theory often work in the simply connected setting, because it's a lot simpler, but I seem to remember that [Griffiths and Morgan "Rational homotopy theory and differential forms" Birkhauser Progress in Mathematics, 16] had a chapter on the fundamental group. It's a bit vague, but I hope it's helpful. Simon Willerton.