Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)

     

Homotopical complexity and good spaces

Author(s): M. Intermont; J. Strom
Journal: Trans. Amer. Math. Soc. 359 (2007), 687-700.
MSC (2000): Primary 55Q05
Posted: August 16, 2006
MathSciNet review: 2255193
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: This paper is an exploration of two ideas in the study of closed classes: the $ A$-complexity of a space $ X$ and the notion of good spaces (spaces $ A$ for which $ \mathcal{C}(A) = \overline{\mathcal{C}(A)}$). A variety of formulae for the computation of complexity are given, along with some calculations. Good spaces are characterized in terms of the functors $ CW_A$ and $ P_A$. The main result is a countable upper bound for $ \Sigma A$-complexity when $ A$ is a good space.

References:

[A]
M. Arkowitz, The generalized Whitehead product, Pacific J. Math. 12 (1962), 7-23. MR 0155328 (27:5262)

[B-K]
A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, SLNM 304 Springer-Verlag, Berlin, 1972. MR 0365573 (51:1825)

[B]
A. K. Bousfield, Localization and periodicity in unstable homotopy theory, J. Am. Math. Soc. 7 (1994), 831-874. MR 1257059 (95c:55010)

[C1]
W. Chachólski, Closed classes, Algebraic topology: new trends in localization and periodicity (Sant Feliu de Guíxols, 1994), 95-118, Progr. Math., 136, Birkhäuser, Basel, 1996. MR 1397724 (97e:55007)

[C2]
W. Chachólski, On the functors $ CW_A$ and $ P_A$, Duke Math. J. 84 (1996), 599-631. MR 1408539 (97i:55023)

[C3]
W. Chachólski, Desuspending and delooping cellular inequalities, Invent. Math. 129 (1997), 37-62. MR 1464865 (98i:55013)

[CDI]
W. Chachólski, W. G. Dwyer and M. Intermont, The $ A$-complexity of a space, J. London Math. Soc. (2) 65 (2002), 204-222. MR 1875145 (2002j:55009)

[CPS]
W. Chachólski, P.-E. Parent and D. Stanley, Cellular generators, Proc. Amer. Math. Soc. 132 (2004), no. 11, 3397-3409. MR 2073317 (2005h:55012)

[Fa1]
E. Dror Farjoun, Cellular Inequalities, The Cech Centennial (Boston, MA, 1993), 159-181, Contemp. Math., 181, AMS, Providence, RI, 1995. MR 1320991 (96g:55011)

[Fa2]
E. Dror Farjoun, Cellular Sapces, Null Spaces, and Homotopy Localization, Springer-Verlag, Berlin, 1996.

[Fr]
A. A. Fraenkel, Abstract Set Theory, North-Holland Publishing Co., Amsterdam, 1966. MR 0197271 (33:5442)

[S]
C. R. Stover, A van Kampen spectral sequence for higher homotopy groups, Topology 29 (1990), 9-26. MR 1046622 (91h:55011)

[W]
G. W. Whitehead, Elements of Homotopy Theory, Graduate Texts in Mathematics 61, Springer-Verlag, 1978. MR 0516508 (80b:55001)

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 55Q05

Retrieve articles in all Journals with MSC (2000): 55Q05

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: 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
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia