Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Witt classes of integral representations of an abelian $ 2$-group


Author: David E. Gibbs
Journal: Proc. Amer. Math. Soc. 70 (1978), 103-108
MSC: Primary 57R85; Secondary 10C05, 15A63, 20C10
MathSciNet review: 492055
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper the Witt groups of integral representations of an abelian 2-group $ \pi ,{W_0}(\pi ;Z)$ and $ {W_2}(\pi ;Z)$ are calculated. Invariants are listed which completely determine $ {W_0}({Z_4};Z)$ and $ {W_2}({Z_4};Z)$ and can be extended to the case $ \pi = {Z_{{2^k}}}$. If $ \pi $ is an elementary abelian 2-group, it is shown that $ {W_2}(\pi ;Z) = 0$ and $ {W_0}(\pi ;Z[\tfrac{1}{2}])$ is ring isomorphic to the group ring $ W(Z[\tfrac{1}{2}])({\operatorname{Hom}}(\pi ,{Z_2}))$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57R85, 10C05, 15A63, 20C10

Retrieve articles in all journals with MSC: 57R85, 10C05, 15A63, 20C10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0492055-1
PII: S 0002-9939(1978)0492055-1
Keywords: Bordism, representation, Witt ring
Article copyright: © Copyright 1978 American Mathematical Society