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The finiteness of NK1(ℤ[G])
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Joachim Grunewald
Veröffentlicht/Copyright:
19. März 2010
Abstract
For a finite group G it was known that the abelian group NK0(ℤG) is always finitely generated over the Verschiebung algebra. This result inspired Connolly and the author to asked the question whether NK1(ℤG) is also finitely generated over the Verschiebung algebra. Based on a computation of Weibel we obtain a negative answer to this question by proving that NK1(ℤ[C2×C2]) is not finitely generated over the larger Verschiebung and Frobenius algebra.
This raises the question of a different finiteness of NK1. In the last part we show that the filtration on NK1(ℤG) which is induced by the degree of a polynomial has the property that the quotients are finite groups.
Received: 2008-03-19
Revised: 2008-05-23
Published Online: 2010-03-19
Published in Print: 2010-March
© de Gruyter 2010
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Artikel in diesem Heft
- Lp estimates for parabolic magnetic Schrödinger operators
- Calculation of UNil for the cyclic group of order two
- Lie theoretic significance of the measure topologies associated with a finite trace
- Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems
- The finiteness of NK1(ℤ[G])
- Poincaré duality pairs of dimension three
- Optimal quantization of probabilities concentrated on small balls
- A sharp diameter bound for unipotent groups of classical type over ℤ/pℤ
- Homological localizations of Eilenberg–MacLane spectra
- A∞-coalgebra structure maps that vanish on H∗(K(π, n); ℤp)
- The cohomology groups of the outer Whitehead automorphism group of a free product
- Dual topology of the motion groups
Artikel in diesem Heft
- Lp estimates for parabolic magnetic Schrödinger operators
- Calculation of UNil for the cyclic group of order two
- Lie theoretic significance of the measure topologies associated with a finite trace
- Integral formulas for a class of curvature PDE's and applications to isoperimetric inequalities and to symmetry problems
- The finiteness of NK1(ℤ[G])
- Poincaré duality pairs of dimension three
- Optimal quantization of probabilities concentrated on small balls
- A sharp diameter bound for unipotent groups of classical type over ℤ/pℤ
- Homological localizations of Eilenberg–MacLane spectra
- A∞-coalgebra structure maps that vanish on H∗(K(π, n); ℤp)
- The cohomology groups of the outer Whitehead automorphism group of a free product
- Dual topology of the motion groups
