Subject: n-cubes question
From: Stefan Forcey <sforcey@mytsu.tnstate.edu>
Date: Thu, 27 Oct 2005 14:39:02 -0500 (CDT)

My question is about the requirement in the definition of the little 
n-cubes operad that in the space of j-cubes the j little cubes are 
disjoint. This does seem to be important in the action of the little 
cubes on an iterated loop space, since intuitively allowing overlapping 
little cubes would preclude in general the continuity of the action. 
  However, allowing overlapping cubes doesn't appear to harm the 
associativity of the operad composition. My question then is about a 
space that allows a traditional little cube action but also seems to 
allow a continuous 
overlapping little cube action. Has such a thing been studied? Does 
such an action imply more or less than recognition of the loop degree 
of said space? 


If anyone is interested in more details about the space I happen to be 
looking at--continuous valued cellular automata--preliminary drafts are 
available at www.math.vt.edu/people/sforcey/automads.pdf