Date: Mon, 27 Apr 1998 08:21:06 -0400 (EDT) From: James Stasheff Subject: for your newsletter - th Query: The ordinary singular cochains form an associative, but only homotopy commutative, algebra. Rationally, you can symmetrize. The symmetrized product will not be associative, but, almost obviously, it will be a homotopy associative. Is it clear that you may define higher coherent homotopies - with precisely the symmetires of what Markl calls a balanced $A_\infty$-algebra? More to the point, is it written somewhere? ************************************************************ Until August 10, 1998, I am on leave from UNC and am at the University of Pennsylvania Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250