Subject: Re: two responses From: Steve Halperin Date: Fri, 13 Aug 2004 12:18:16 -0400 (Eastern Daylight Time) My recollection is that Sullivan's Infinitesimal Computations does have a section on this, and that one recovers the rationalization of the lower central series of the fundamental group as a graded Lie algebra. There may be a finiteness hypothesis somewhere. Sullivan may not have provided complete proofs, but I have seen such, not sure where. Steve Halperin On Fri, 13 Aug 2004 10:57:45 -0400 Don Davis wrote: >> 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. >> >> ---------------------- Steve Halperin, Dean shalper@deans.umd.edu