3 similar responses to Stasheff question....DMD ___________________- Date: Tue, 16 Nov 1999 20:56:02 -0500 (EST) From: Joseph Roitberg Subject: Re: question about U(n) Both results are proved in: Ioan James & Emery Thomas, "Which Lie groups are homotopy-abelian?", Proc Natl Acad Sci 45 (1959), 737-740. (Similar results are obtained in the real orthogonal and symplectic cases.) See also Raoul Bott's paper "A report on the unitary group", Proc Symp Pure Math (Differential Geometry), Vol III (1961), 1-6, interesting for its geometric approach and also for its taunting of algebraic topology. Joe Roitberg On Tue, 16 Nov 1999, DON DAVIS wrote: > Date: Tue, 16 Nov 1999 09:23:55 -0500 (EST) > From: James Stasheff > Subject: query > > U(n) is homotopy commutative within U(2n) > anyone recall who first observed that in print? > do I recall correctly that U(n) is not homtopy commutative inside U(2n-1)? > reference? > thanks > > Jim Stasheff jds@math.upenn.edu > Until Dec 1999, I will be visiting U Penn but for hard copy > the relevant address is: > 146 Woodland Dr > Lansdale PA 19446 (215)822-6707 > > As of Jan 3, 00 > > Jim Stasheff jds@math.unc.edu > Math-UNC (919)-962-9607 > Chapel Hill NC FAX:(919)-962-2568 > 27599-3250 > > > From jimlin@euclid.UCSD.Edu Tue Nov 16 15:25:57 1999 Date: Tue, 16 Nov 1999 12:25:47 -0800 From jimlin@euclid.UCSD.Edu Tue Nov 16 15:25:57 1999 Date: Tue, 16 Nov 1999 12:25:47 -0800 To: dmd1@lehigh.edu (DON DAVIS) From: Jim Lin Subject: Re: question about U(n) Jim- The first place I saw this fact was in the paper by Ioan James and Emery Thomas, Which Lie groups are homotopy-abelian?, Proc. Nat'l Academy, v. 45, no.5, 737-740. Yes, U(n) is not homotopy commutative in U(2n-1). Jim Lin ______________ From Martin.A.Arkowitz@Dartmouth.EDU Tue Nov 16 17:32:54 1999 Date: 16 Nov 1999 17:32:54 EST From: Martin.A.Arkowitz@Dartmouth.EDU (Martin A. Arkowitz) Subject: Re: question about U(n) Don, Regarding Jim Stasheff's question: James and Thomas prove in Proc. Nat. Acad. Sci. Vol. 45 (1959), pp. 737-740 that U(n) is not homotopy-abelian in U(2n-1) and observe that U(n) is homotopy-abelian in U(2n). --Martin To: dmd1@lehigh.edu (DON DAVIS) From: Jim Lin Subject: Re: question about U(n) Jim- The first place I saw this fact was in the paper by Ioan James and Emery Thomas, Which Lie groups are homotopy-abelian?, Proc. Nat'l Academy, v. 45, no.5, 737-740. Yes, U(n) is not homotopy commutative in U(2n-1). Jim Lin >Date: Tue, 16 Nov 1999 09:23:55 -0500 (EST) >From: James Stasheff >Subject: query > >U(n) is homotopy commutative within U(2n) >anyone recall who first observed that in print? >do I recall correctly that U(n) is not homtopy commutative inside U(2n-1)? >reference? >thanks > > Jim Stasheff jds@math.upenn.edu > Until Dec 1999, I will be visiting U Penn but for hard copy > the relevant address is: > 146 Woodland Dr > Lansdale PA 19446 (215)822-6707 > > As of Jan 3, 00 > > Jim Stasheff jds@math.unc.edu > Math-UNC (919)-962-9607 > Chapel Hill NC FAX:(919)-962-2568 > 27599-3250