Isomorphism Conjectures in Algebraic K-Theory

Farrell, F. T.; Jones, L. E.

doi:10.2307/2152801

Cited by 159 publications

(306 citation statements)

References 13 publications

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“…The p-chain spectral sequence is an important tool for integral computations which are much harder. More information about these conjectures can be found for instance in [2], [12], [22] and [31].…”

Section: Review Of Spaces Over a Category And Assembly Mapsmentioning

confidence: 99%

The p-chain Spectral Sequence

Davis¹,

Lueck²

2003

K-Theory

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We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah-Hirzebruch type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum-Connes and Farrell-Jones to compute algebraic K-and L-groups of group rings and topological K-groups of reduced group C * -algebras.

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Section: Review Of Spaces Over a Category And Assembly Mapsmentioning

confidence: 99%

The p-chain Spectral Sequence

Davis¹,

Lueck²

2003

K-Theory

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“…On the other hand, we do not know how to prove Theorem 7.1 for fields of characteristic different from 2; for example we do not know how to prove Theorem 7.1 in the case k = k 3 . See [18,Appendix] for details about universal Γ-spaces relative to a class of subgroups of Γ.…”

Section: Whitehead Groups Of Solvable Linear Groupsmentioning

confidence: 99%

Whitehead groups and the Bass conjecture

Farrell

Linnell

2003

Mathematische Annalen

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“…Since we want to do this in the language of spaces and spectra over a category we give some basic facts about these notions. More information can be found for instance in [15], [18].…”

Section: Review Of the Isomorphism Conjectures In K-and L-theorymentioning

confidence: 99%

“…Notice that for n = ∞ and m = 1 it is just [18,Theorem A.10]. Theorem 2.3 Let F ⊂ G be families of subgroups of the group G. For H ∈ G define the family H ∩ F := {K ∩ H | K ∈ F } of subgroups of H. Let E be an Or(G)-spectrum.…”

Section: Preliminaries About Spaces Over the Orbit Categorymentioning

confidence: 99%

Computations of K- and L-Theory of Cocompact Planar Groups

Wolfgang

Stamm²

2000

K-Theory

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Using the isomorphism conjectures of Baum & Connes and Farrel & Jones, we compute the algebraic K-and L-theory and the topological K-theory of cocompact planar groups (= cocompact N.E.C-groups) and of groups G appearing in an extension 1 → Z n → G → π → 1 where π is a finite group and the conjugation π-action on Z n is free outside 0 ∈ Z n . These computations apply for instance to two-dimensional crystallographic groups and cocompact Fuchsian groups.

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Isomorphism Conjectures in Algebraic K-Theory

Cited by 159 publications

References 13 publications

The p-chain Spectral Sequence

The p-chain Spectral Sequence

Whitehead groups and the Bass conjecture

Computations of K- and L-Theory of Cocompact Planar Groups

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