Projective Dimension in Filtrated K-Theory

Rasmus Moritz Bentmann

doi:10.1007/978-3-642-39459-1_3

Projective Dimension in Filtrated K-Theory

Rasmus Moritz Bentmann

Department of Mathematical Sciences

1 Citation (Scopus)

Abstract

Under mild assumptions, we characterise modules with projective resolutions of length n ∈ ℕ in the target category of filtrated K-theory over a finite topological space in terms of two conditions involving certain Tor-groups. We show that the filtrated K-theory of any separable C ^*dash-algebra over any topological space with at most four points has projective dimension 2 or less. We observe that this implies a universal coefficient theorem for rational equivariant KK-theory over these spaces. As a contrasting example, we find a separable C ^*dash-algebra in the bootstrap class over a certain five-point space, the filtrated K-theory of which has projective dimension 3. Finally, as an application of our investigations, we exhibit Cuntz-Krieger algebras which have projective dimension 2 in filtrated K-theory over their respective primitive spectrum.

Original language	English
Title of host publication	Operator Algebra and Dynamics : Nordforsk Network Closing Conference, Faroe Islands, May 2012
Editors	Toke M. Clausen, Søren Eilers, Gunnar Restorff, Sergei Silvestrov
Publisher	Springer
Publication date	2013
Pages	41-62
ISBN (Print)	9783642394584
ISBN (Electronic)	9783642394591
DOIs	https://doi.org/10.1007/978-3-642-39459-1_3
Publication status	Published - 2013

Series	Springer Proceedings in Mathematics & Statistics
Volume	58

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10.1007/978-3-642-39459-1_3

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Projective Dimension in Filtrated K-Theory. / Bentmann, Rasmus Moritz.

Operator Algebra and Dynamics: Nordforsk Network Closing Conference, Faroe Islands, May 2012. ed. / Toke M. Clausen; Søren Eilers; Gunnar Restorff; Sergei Silvestrov. Springer, 2013. p. 41-62 (Springer Proceedings in Mathematics & Statistics , Vol. 58).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Projective Dimension in Filtrated K-Theory

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