Yesterday, Jim McClure asked about cup-i products. Here are three responses..........DMD _____________________________________________________ Date: Wed, 12 May 1999 07:35:33 +0100 From: Subject: Jim's question At p=2 there's a formula which I think is due to Steenrod. For the Alexander-Whitney cup product you look at pairs of maps {0,..,n} ---> {0,..,n+m} <--- {0,..,m} whose images fit together like this: *********** ****************** For the cup-i product you look at maps {0,..,n} ---> {0,..,n+m-i} <--- {0,..,m} whose images fit together like this: ******* *********** **** ***** *********** (with i-1 overlaps). Someone Chinese whose name I don't remember generalised this to odd primes, but it becomes horrible. I think I saw all this in the two big volumes of old references in topology in the MIT reading room, unfortunately that's the best reference I can give. Neil _____________________________________________ Subject: McClure-Question Date: Wed, 12 May 1999 10:09:58 +0200 From: Christian Nassau I remember seeing an explicit extended diagonal approximation in Dave Benson's "Representations and Cohomology, Vol II"; he deals with the bar resolution in group cohomology, but his formulas should be valid more generally. --------- Christian Nassau e-mail: nassau@math.uni-frankfurt.de home-page: http://www.math.uni-frankfurt.de/~nassau Fachbereich Mathematik (12) AG 8.1, Zi.905 Johann Wolfgang Goethe-Universit"at Robert-Mayer-Str. 6-10 D-60054 Frankfurt/M --- Germany --- ______________________________________________________________ Date: Wed, 12 May 1999 08:47:32 -0400 (EDT) From: James Stasheff Subject: Re: question & job anncmt Ouch! that makes me feel old! See Steenrod's original treatment where the formulas are as explicit as can be the jazz came much later and Steenrod wass at first less that impressed those explicit formulas are what motivated Gerstenhaber to produce a cup_1 in the Hochschild complex .oooO Jim Stasheff jds@math.unc.edu (UNC) Math-UNC (919)-962-9607 \ ( Chapel Hill NC FAX:(919)-962-2568 \*) 27599-3250 http://www.math.unc.edu/Faculty/jds