Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the $ K$-theory of crystallographic groups


Author: Georgios Tsapogas
Journal: Trans. Amer. Math. Soc. 347 (1995), 2781-2794
MSC: Primary 19D35; Secondary 20H15, 57Q10
DOI: https://doi.org/10.1090/S0002-9947-1995-1308025-1
MathSciNet review: 1308025
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For any crystallographic group $ \Gamma $ we show that the groups $ {K_i}(\Gamma )$ are isomorphic, via the forget control map, to the controlled $ K$-groups $ {K_i}{(\Gamma )_c}$, for all $ i \leqslant 1$ and for an appropriate choice of the control map. By using this result and under a mild hypothesis on the crystallographic group $ \Gamma $, it is proved that $ {K_i}(\Gamma ) = 0$ for all $ i \leqslant - 2$ and $ {N^j}{K_i}(\Gamma ) = 0$ for all $ i \leqslant - 1$ and $ j > 0$.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 19D35, 20H15, 57Q10

Retrieve articles in all journals with MSC: 19D35, 20H15, 57Q10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1308025-1
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society