Hostname: page-component-cb9f654ff-5kfdg Total loading time: 0 Render date: 2025-08-21T10:08:27.516Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite Complexes and Integral Representations II

Published online by Cambridge University Press:  20 November 2018

James A. Schafer
James A. Schafer*
Affiliation:
Department of Mathematics and Institute for Physical Sciences and Technology University of Maryland College Park, Maryland Department of Mathematics University of Aarhus
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the paper "Finite complexes and integral representations" [Illinois Journal of Math, 26, (1982), p 442] an exact sequence relating homotopy types of (G, d)-complexes with objects of integral representation theory together with some known calculations seemed to imply that the group of homotopy types of (G, d)- complexes was always a subquotient of (ℤ|g|)*. This paper gives a new characterization of one of the terms of the above sequence that allows one to conclude that this is not generally true.

Keywords

55P1555U1518G35

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 1 , 01 March 1984 , pp. 3 - 9
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Browning, W., Homotopy types of certain finite CW-complexes with finite fundamental group, Ph.D. thesis, Cornell University, Ithaca, New York, 1979.Google Scholar
2. Dyer, M. L., Homotopy classification of (IT, m) complexes, J. Pure and Applied Algebra 7 (1976) p. 249.Google Scholar
3. MacLane, S. and Whitehead, J. H. C., On the 3 type of a complex. Proc. Nat. Acad. Sci., U.S.A., 36 (1950) p. 41.Google Scholar
4. Metzler, W., Über den Homotopietyp Zweidimensionaler CW-komplexes und Elementartransformationen bei definierende Relationen. J. reine angewandte Math., 285 (1976), p. 7.Google Scholar
5. Reiner, I., Maximal Orders, Academic Press, London, New York, 1975.Google Scholar
6. Schafer, J., Finite complexes and integral representations. Illinois Journal of Mathematics 26 (1982), p. 407.Google Scholar
7. Sieradski, A., A semigroup of simple homotopy types. Math. Z., 153 (1977), p. 135.Google Scholar
8. Sieradski, A. and Dyer, M. L., Distinguishing arithmetic for certain stably isomorphic modules, J. Pure and Applied Algebra 15 (1979), p. 199.Google Scholar
9. Swan, R., Periodic resolutions for finite groups. Annals of Math. 72 (1960), p. 267.Google Scholar
10. Taylor, M. J., Locally free classgroups of groups of prime power order. Journal of Algebra 50 (1978), p. 463.Google Scholar
11. Wall, C. T. C., Finiteness conditions for CW complexes, II. Proc. Roy. Soc, Ser. A 295 (1966), p. 129.Google Scholar
12. Ullam, S., Non trivial lower bounds for class groups of integral group rings, 111. Journal of Math., 20 (1976), p. 314.Google Scholar
13. Roggenkamp, K. W., and Huber-Dyson, V., Lattices over Orders I, II, Springer Lecture Note Series 115, 142. Berlin and New York, 1970.Google Scholar