Transactions of the American Mathematical Society

Author(s): Hans-Joachim Baues
Journal: Trans. Amer. Math. Soc. 351 (1999), 429-475.
MSC (1991): Primary 55N35, 55Q70, 55S20
Retrieve article in: PDF
This article is available free of charge

Abstract: We describe axioms for a `quadratic homology theory' which generalize the classical axioms of homology. As examples we consider quadratic homology theories induced by 2-excisive homotopy functors in the sense of Goodwillie and the homology of a space with coefficients in a square group which generalizes the homology of a space with coefficients in an abelian group.

1.: Arone, G. and Mahowald, M., The Goodwillie tower of the identity functor and the unstable periodic homotopy of spheres, Preprint (1995), Northwestern University.
2.: Baues, H.J., Obstruction theory, LNM 628, Springer Verlag, 1977. MR 57:7600
3.: Baues, H.J., Algebraic homotopy, Cambridge University Press, 1989. MR 90i:55016
4.: Baues, H.J., Metastable homotopy and homology, Quaestiones Matematicae 14, 1991, pp. 161-178. MR 92j:55012
5.: Baues, H.J., Quadratic functors and metastable homotopy, J. Pure Appl. Algebra 91, 1994, pp. 49-107. MR 94j:55022
6.: Baues, H.J., Combinatorial Homotopy and 4-dimensional Complexes, de Gruyter, Berlin, 1991. MR 92h:55008
7.: Baues, H.J., Homotopy type and homology, Oxford Mathematical Monographs, 500 pages, Oxford University Press, 1996. MR 97f:55001
8.: Baues, H.J. and Conduché, D., On the 2-type of an iterated loop space, Preprint Max-Planck-Institut für Mathematik 95-112.
9.: Baues, H.J. and Hartl, M. and Pirashvili, T., Quadratic categories and square rings, J. Pure Appl. Algebra 122, 1997, pp. 1-40. CMP 98:04
10.: Baues, H.J. and Pirashvili, T., Quadratic endofunctors of the catgeory of groups, Preprint MPI für Math. 95-55.
11.: Baues, H.J. and Pirashvili, T., The universal coefficient theorem for quadratic functors, Preprint MPI für Math. 95-57.
12.: Bousfield, A.K. and Kan, D.M., Homotopy Limits, Completions and Localizations, LNM 304 Springer Verlag, 1972. MR 51:1825
13.: Cohen, F.R. and May, J.P. and Taylor, L.R., Splitting of certain spaces , Math. Proc. Camb. Phil. Soc., (1978), 84, pp. 465-496. MR 80a:55010
14.: Conduché, D., Modules croisés généralisés de longueur 2, J. Pure and Appl. Algebra 34, 1984, pp. 155-178. MR 86g:20068
15.: Curtis, E.B., Simplicial homotopy theory, Advances in Math. 6, 1971, pp. 107-209. MR 43:5529
16.: Dold, A. and Puppe, D., Homologie nicht-additiver Funktoren, Anwendungen, Ann. Inst. Fourier Grenoble 11, 1961, pp. 201-312. MR 27:186
17.: Goodwillie, T.G., Calculus I: the first derivative of pseudoisotopy theory, $K$ -Theory 4, 1990, pp. 1-27. MR 92m:57027
18.: Goodwillie, T.G., Calculus II: analytic functors, $K$ -Theory 5, 1992, pp. 295-332. MR 93i:55015
19.: Goodwillie, T.G., Calculus III: the Taylor series of a homotopy functor, in preparation.
20.: Goodwillie, T.G., The calculus of functors, Preprint 1986 Brown University.
21.: Goodwillie, T.G., Calculus I. The first derivative of a homotopy functor, Preprint Brown University.
22.: Gray, B., Homotopy theory, Academic Press, 1975. MR 53:6528
23.: James, J., On the suspension triad, Ann. of Math. (2) 63, 1956, pp. 191-247. MR 17:1117b
24.: Johnson, B., The derivatives of homotopy theory, Trans. AMS 347, 1995, pp. 1295-1310. MR 96b:55012
25.: Kan, D.M., A relation between CW-complexes and free C.s.s. groups, Amer. J. Math. 81, 1959, pp. 521-528. MR 22:1901
26.: Kan, D.M., A combinatorial definition of homotopy groups, Annals of Math. 67, 1958, pp. 282-312. MR 22:1897
27.: Mac Lane, S., Homology, Academic Press, 1963. MR 28:122
28.: Whitehead, G.W., Recent advances in homotopy theory, AMS Regional Conference Series in Math. 5, 1970. MR 46:8208
29.: Whitehead, G.W., Elements of homotopy theory, Graduate Texts in Math. 61, Springer Verlag, 1978. MR 80b:55001

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 55N35, 55Q70, 55S20

Hans-Joachim Baues
Affiliation: Max-Planck-Institut für Mathematik, Gottfried-Claren-Strasse 26, D-53225 Bonn, Germany
Email: bauses@mpim-bonn.mpg.de

DOI: 10.1090/S0002-9947-99-02335-1
PII: S 0002-9947(99)02335-1
Keywords: Quadratic functors, Goodwillie calculus, Steenrod squares, EHP-sequence
Received by editor(s): October 22, 1996
Copyright of article: Copyright 1999, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS