Premium
The A ‐Complexity of a Space
Author(s) -
Chachólski W.,
Dwyer W. G.,
Intermont M.
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610701002691
Subject(s) - space (punctuation) , construct (python library) , homotopy , mathematics , theoretical computer science , computer science , algorithm , discrete mathematics , pure mathematics , programming language , operating system
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 CW A ( X ) of an arbitrary space X .