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Homotopical complexity and good spaces
Authors:
M. Intermont and J. Strom
Journal:
Trans. Amer. Math. Soc. 359 (2007), 687-700
MSC (2000):
Primary 55Q05
Posted:
August 16, 2006
MathSciNet review:
2255193
Full-text PDF Free Access
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Abstract: This paper is an exploration of two ideas in the study of closed classes: the  -complexity of a space  and the notion of good spaces (spaces  for which  ). A variety of formulae for the computation of complexity are given, along with some calculations. Good spaces are characterized in terms of the functors  and  . The main result is a countable upper bound for  -complexity when  is a good space.
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- [C2]
- W. Chachólski, On the functors
 and  , Duke Math. J. 84 (1996), 599-631. MR 1408539 (97i:55023)
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- W. Chachólski, Desuspending and delooping cellular inequalities, Invent. Math. 129 (1997), 37-62. MR 1464865 (98i:55013)
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- E. Dror Farjoun, Cellular Sapces, Null Spaces, and Homotopy Localization, Springer-Verlag, Berlin, 1996.
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- A. A. Fraenkel, Abstract Set Theory, North-Holland Publishing Co., Amsterdam, 1966. MR 0197271 (33:5442)
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- G. W. Whitehead, Elements of Homotopy Theory, Graduate Texts in Mathematics 61, Springer-Verlag, 1978. MR 0516508 (80b:55001)
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Additional Information
M. Intermont
Affiliation:
Department of Mathematics, Kalamazoo College, Kalamazoo, Michigan 49006
Email:
intermon@kzoo.edu
J. Strom
Affiliation:
Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008
Email:
Jeff.Strom@wmich.edu
DOI:
http://dx.doi.org/10.1090/S0002-9947-06-03890-6
PII:
S 0002-9947(06)03890-6
Keywords:
Closed class,
complexity,
homotopy colimit
Received by editor(s):
June 10, 2004
Received by editor(s) in revised form:
November 23, 2004
Posted:
August 16, 2006
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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