The A-complication of a space
W. Chacholski, W. G. Dwyer, and M. Intermont
Suppose that A is a pointed CW-complex. We look at how difficult
it is to construct an A-cellular space B from copies of A by
repeatedly taking homotopy colimits; this is determined by an ordinal
number called the complication of B. Studying the complication
leads to an iterative technique, based on resolutions, for
constructing the A-cellular approximation CW_A(X) of an arbitrary
space X.
Yale University, New Haven, CT 06520 USA
University of Notre Dame, Notre Dame IN 46556 USA
Kalamazoo College, Kalamazoo MI, 49006 USA
MSC2000: 55P60, 55P99