Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-11T02:23:30.287Z Has data issue: false hasContentIssue false
  • English
  • Français

Periodicity theorems and conjectures in hermitian K-theory

Published online by Cambridge University Press:  03 September 2009

Max Karoubi
Max Karoubi
Affiliation:
Université Paris Diderot/Paris 7UFR de mathématiques case 7012, 175 rue du Chevaleret, 75205 Paris Cedex 13, France, max.karoubi@gmail.com.
Get access

Abstract

In this appendix to [4], we state a periodicity conjecture using form parameters. This conjecture contains as particular case the fundamental theorem in hermitian K-theory proved in [6] but also some results of Bak [1], Barge and Lannes [2], Sharpe [8], for lower hermitian K-groups. The interest of this conjecture lies also in the parallel use of hermitian forms and quadratic forms with form parameters introduced by Bak.

Keywords

Bott periodicityhermitian formsquadratic formshermitian K-theory
Type
Research Article
Information
Journal of K-Theory , Volume 4 , Issue 1 , August 2009 , pp. 67 - 75
Copyright
Copyright © ISOPP 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bak, A., K-theory of Forms. Annals of Mathematics Studies 98, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1981Google Scholar
2.Barge, J.; Lannes, J., Suites de Sturm, indice de Maslov et périodicité de Bott, To appear.Google Scholar
3.Clauwens, F. J. -B. J, The K-theory of almost symmetric forms. Topological structures, II (Proc. Sympos. Topology and Geom., Amsterdam, 1978), Part 1, pp. 41–49, Math. Centre Tracts 115, Math. Centrum, Amsterdam, 1979Google Scholar
4.Hazrat, R.; Vavilov, N., Bak's work on the K-theory of rings, J. K-Theory 4(2009), 1–65.CrossRefGoogle Scholar
5.Karoubi, M., Periodicity theorems in topological, algebraic and hermitian K-theory, K-theory handbook, Springer-Verlag (2005), pp.111–137.CrossRefGoogle Scholar
6.Karoubi, M., Le théoréme fondamental de la K-théorie hermitienne. (French) Ann. of Math. (2) 112 (1980), no. 2, 259–282.CrossRefGoogle Scholar
7.Karoubi, M.; Villamayor, O., K-théorie algébrique et K-théorie topologique. II. (French) Math. Scand. 32 (1973), 57–86.CrossRefGoogle Scholar
8.Sharpe, R., On the structure of the unitary Steinberg groups. Ann. Math. 96 (1972), 444–479.CrossRefGoogle Scholar