C*-algebras over topological spaces: filtrated K-theory
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
C*-algebras over topological spaces : filtrated K-theory. / Meyer, Ralf; Nest, Ryszard.
I: Canadian Journal of Mathematics - Journal Canadien de Mathématiques, Bind 64, Nr. 2, 2012, s. 368-408.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - C*-algebras over topological spaces
T2 - filtrated K-theory
AU - Meyer, Ralf
AU - Nest, Ryszard
PY - 2012
Y1 - 2012
N2 - We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with a totally ordered lattice of open subsets, this spectral sequence becomes an exact sequence as in the Universal Coefficient Theorem, with the same consequences for classification. We also exhibit an example where filtrated K-theory is not yet a complete invariant. We describe two C*-algebras over a space X with four points that have isomorphic filtrated K-theory without being KK(X)-equivalent. For this space X, we enrich filtrated K-theory by another K-theory functor to a complete invariant up to KK(X)-equivalence that satisfies a Universal Coefficient Theorem.
AB - We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with a totally ordered lattice of open subsets, this spectral sequence becomes an exact sequence as in the Universal Coefficient Theorem, with the same consequences for classification. We also exhibit an example where filtrated K-theory is not yet a complete invariant. We describe two C*-algebras over a space X with four points that have isomorphic filtrated K-theory without being KK(X)-equivalent. For this space X, we enrich filtrated K-theory by another K-theory functor to a complete invariant up to KK(X)-equivalence that satisfies a Universal Coefficient Theorem.
U2 - 10.4153/CJM-2011-061-x
DO - 10.4153/CJM-2011-061-x
M3 - Journal article
VL - 64
SP - 368
EP - 408
JO - Canadian Journal of Mathematics - Journal Canadien de Mathématiques
JF - Canadian Journal of Mathematics - Journal Canadien de Mathématiques
SN - 0008-414X
IS - 2
ER -
ID: 45182486