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THE A-COMPLEXITY OF A SPACE

Published online by Cambridge University Press:  06 March 2002

W. CHACHÓLSKI ,
W. G. DWYER  and
M. INTERMONT
W. CHACHÓLSKI
Affiliation:
Yale University, New Haven, CT 06520, USA; [email protected]
W. G. DWYER
Affiliation:
University of Notre Dame, Notre Dame, IN 46556, USA; [email protected]
M. INTERMONT
Affiliation:
Kalamazoo College, Kalamazoo, MI 49006, USA; [email protected]
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Abstract

Suppose that A is a pointed CW-complex. The paper looks 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 complexity of B. Studying the complexity leads to an iterative technique, based on resolutions, for constructing the A-cellular approximation CWA(X) of an arbitrary space X.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 204 - 222
Copyright
2002 London Mathematical Society

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