On the exponent of the cokernel of the forget-control map on K<sub>0</sub>-groups

Connolly, Francis X.; Prassidis, Stratos

doi:10.4064/fm172-3-1

Cited by 9 publications

(4 citation statements)

References 18 publications

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“…They vanish rationally, in dimension 0 by [76] and in higher dimensions by [182]. For more information see also [75]. Analogously to the proof of Proposition 2.14 we obtain the following proposition.…”

Section: Splitting Off Nil-terms and Rationalized Algebraic K-theorysupporting

confidence: 67%

The Baum–Connes and the Farrell–Jones Conjectures in K- and L-Theory

Lück

Reich

2005

Handbook of K-Theory

161

179

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Section: Splitting Off Nil-terms and Rationalized Algebraic K-theorysupporting

confidence: 67%

The Baum–Connes and the Farrell–Jones Conjectures in K- and L-Theory

Lück

Reich

2005

Handbook of K-Theory

161

179

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“…Therefore, we can write G ∼ = G 1 * F G 2 , where F has square-free order and index two in both factors, and both G 1 and G 2 are isomorphic to subgroups of S 4 . By results of [Wal78] (see also [CP02]),…”

Section: Next Observe That We Have Obvious γ-Equivariant Homotopy Equ...mentioning

confidence: 88%

The Lower Algebraic K-Theory of Split Three-Dimensional Crystallographic Groups

Farley,

Ortiz

2012

Preprint

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We compute K −1 , K 0 , and the Whitehead groups of all threedimensional crystallographic groups Γ which fit into a split extensionwhere H is a finite group acting effectively on Z 3 . Such groups Γ account for 73 isomorphism types of three-dimensional crystallographic groups, out of 219 types in all.We also prove a general splitting formula for the lower algebraic K-theory of all three-dimensional crystallographic groups, which generalizes the one for the Whitehead group obtained by Alves and Ontaneda.

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“…It is well known that the Nil-groups associated to virtually cyclic groups are either trivial or infinitely generated (see [F77], [G1], [R]). Furthermore, these groups are known to be purely torsion (see [We81], [CP02], [KT03], [G2]), giving us the second statement.…”

Section: Discussionmentioning

confidence: 99%

Splitting formulas for certain Waldhausen Nil-groups

Lafont¹,

Ortiz²

2009

Journal of the London Mathematical Society

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Abstract. We provide splitting formulas for certain Waldhausen Nil-groups. We focus on Waldhausen Nil-groups associated to acylindrical amalgamations Γ = G 1 * H G 2 of groups G 1 , G 2 over a common subgroup H. For these amalgamations, we explain how, provided G 1 , G 2 , Γ satisfy the Farrell-Jones isomorphism conjecture, the Waldhausen Nil-groupscan be expressed as a direct sum of Nil-groups associated to a specific collection of virtually cyclic subgroups of Γ. A special case covered by our theorem is the case of arbitrary amalgamations over a finite group H.

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On the exponent of the cokernel of the forget-control map on K₀-groups

Cited by 9 publications

References 18 publications

The Baum–Connes and the Farrell–Jones Conjectures in K- and L-Theory

The Baum–Connes and the Farrell–Jones Conjectures in K- and L-Theory

The Lower Algebraic K-Theory of Split Three-Dimensional Crystallographic Groups

Splitting formulas for certain Waldhausen Nil-groups

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On the exponent of the cokernel of the forget-control map on K0-groups

Cited by 9 publications

References 18 publications

The Baum–Connes and the Farrell–Jones Conjectures in K- and L-Theory

The Baum–Connes and the Farrell–Jones Conjectures in K- and L-Theory

The Lower Algebraic K-Theory of Split Three-Dimensional Crystallographic Groups

Splitting formulas for certain Waldhausen Nil-groups

Contact Info

Product

Resources

About

On the exponent of the cokernel of the forget-control map on K₀-groups