Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-24T01:43:32.610Z Has data issue: false hasContentIssue false
  • English
  • Français

Hermitian periodicity and cohomology of infinite orthogonal groups

Published online by Cambridge University Press:  23 May 2013

A. J. Berrick ,
M. Karoubi  and
P. A. Østvær
A. J. Berrick
Affiliation:
Department of Mathematics, National University of Singapore and Yale-NUS College, [email protected], [email protected]
M. Karoubi
Affiliation:
UFR de Mathématiques, Université Paris 7, [email protected]
P. A. Østvær
Affiliation:
Department of Mathematics, University of Oslo, [email protected]
Get access

Abstract

As an application of our papers in hermitian K-theory, in favourable cases we prove the periodicity of hermitian K-groups with a shorter period than previously obtained. We also compute the homology and cohomology with field coeffcients of infinite orthogonal and symplectic groups of specific rings of integers in a number field.

Keywords

Periodicityhermitian K-theorygroup cohomology19D50
Type
Research Article
Information
Journal of K-Theory , Volume 12 , Issue 1: Nanjing Special Issue on K-theory, number theory and geometry , August 2013 , pp. 203 - 211
Copyright
Copyright © ISOPP 2013 

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.Berrick, A. J. and Karoubi, M.. Hermitian K-theory of the integers. Amer. J. Math. 127 (2005), 785–823.CrossRefGoogle Scholar
2.Berrick, A. J., Karoubi, M., and Østvær, P. A.. Hermitian K-theory and 2-regularity for totally real number fields. Math. Annalen 349 (2011), 117–159.Google Scholar
3.Berrick, A. J., Karoubi, M., Østvær, P. A. and Schlichting, M.. The homotopy fixed point theorem and the Quillen-Lichtenbaum conjecture in hermitian K-theory. ArXiv Math:1011.4977.Google Scholar
4.Berrick, A. J., Karoubi, M., and Østvær, P. A.. Periodicity of hermitian K-groups. Journal of K-Theory 7 (2011), 429–493.Google Scholar
5.Borel, A.. Stable real cohomology of arithmetic groups. Ann. Sci. École Norm. Sup. (4) 7 (1975), 235–272.CrossRefGoogle Scholar
6.and, Z. FiedorowiczPriddy, S.. Homology of Classical Groups over Finite Fields and Their Associated Infinite Loop Spaces. Lecture Notes in Math. 674, Springer, (New York, 1978).Google Scholar
7.Karoubi, M.. Le théorème fondamental de la K-théorie hermitienne. Ann. of Math. (2), 112 (1980), 259–282.CrossRefGoogle Scholar
8.Karoubi, M.. Relations between algebraic K-theory and hermitian K-theory. Journal of Pure and Applied Algebra 34 (1984), 259–263.CrossRefGoogle Scholar
9.McCleary, J.. A User's Guide to Spectral Sequences. Cambridge Studies in Advanced Math. 58, Cambridge Univ. Press, (Cambridge, 2001).Google Scholar
10.Milnor, J. & Husemoller, D.: Symmetric Bilinear Forms, Ergeb. Math. 73, Springer, (Berlin, 1973).CrossRefGoogle Scholar
11.Quillen, D.. Letter from Quillen to Milnor on Im(πi(O) → πsi → Ki(ℤ)). In Algebraic K-Theory, Lecture Notes in Math. 551, Springer (New York, 1976), 182–188.Google Scholar
12.Switzer, R. M.. Algebraic Topology – Homology and Homotopy. Classics in Math., Springer, 2002.Google Scholar