Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Extending cellular cohomology to $ C\sp *$-algebras


Authors: Ruy Exel and Terry A. Loring
Journal: Trans. Amer. Math. Soc. 329 (1992), 141-160
MSC: Primary 46L80; Secondary 19K56, 46M20, 58A10, 58G12
MathSciNet review: 1024770
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A filtration on the $ K$-theory of $ {C^*}$-algebras is introduced. The relative quotients define groups $ {H_n}(A),n \geq 0$, for any $ {C^*}$-algebra $ A$, which we call the spherical homology of $ A$. This extends cellular cohomology in the sense that

$\displaystyle {H_n}(C(X)) \otimes {\mathbf{Q}} \cong {H^n}(X;{\mathbf{Q}})$

for $ X$ a finite CW-complex. While no extension of cellular cohomology which is derived from a filtration on $ K$-theory can be additive, Morita-invariant, and continuous, $ {H_n}$ is shown to be infinitely additive, Morita invariant for unital $ {C^*}$-algebras, and continuous in limited cases.

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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46L80, 19K56, 46M20, 58A10, 58G12

Retrieve articles in all journals with MSC: 46L80, 19K56, 46M20, 58A10, 58G12


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1024770-7
PII: S 0002-9947(1992)1024770-7
Keywords: $ {C^*}$-algebras, homology, $ K$-theory, filtration, determinant
Article copyright: © Copyright 1992 American Mathematical Society