Yesterday, Jim McClure asked about cup-i products.  Here are three
responses..........DMD
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Date: Wed, 12 May 1999 07:35:33 +0100
From: <N.P.Strickland@sheffield.ac.uk>
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 <nassau@math.uni-frankfurt.de>

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 <jds@math.unc.edu>
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
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