The surgery obstruction groups of the infinite dihedral group

Connolly, Francis X.; Davis, James F.

doi:10.2140/gt.2004.8.1043

Cited by 21 publications

(38 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Because of Corollary 3.6 and assumption (VCL) it suffices to check that the following assembly map is an isomorphism (c) The proof is analogous to the one of assertion (b) using the conclusion from [34] that for any virtually cyclic group V the assembly map There a term UNIL appears which has meanwhile been computed by Connolly and Davis [8]. The computation of Wh q (F ) for a Fuchsian groups F for q ≤ 1 was independently carried out in [3] and [4] using the p-chain spectral sequence.…”

Section: Definition 311mentioning

confidence: 99%

The p-chain Spectral Sequence

Davis¹,

Lueck²

2003

K-Theory

View full text Add to dashboard Cite

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.

show abstract

Section: Definition 311mentioning

confidence: 99%

The p-chain Spectral Sequence

Davis¹,

Lueck²

2003

K-Theory

View full text Add to dashboard Cite

show abstract

“…2 Remark 2.2. Connolly-Davis ( [7]) completed the computation of L n (Z/2 * Z/2, ω) for all n and all orientation characters ω. As a result, one can modify the above construction using orientation reversing involutions on tori with isolated fixed sets, to produce different examples.…”

Section: H )mentioning

confidence: 99%

On the generalized Nielsen realization problem

Block¹,

Weinberger²

2008

Comment. Math. Helv.

View full text Add to dashboard Cite

Abstract. The main goal of this paper is to give the first examples of equivariant aspherical Poincaré complexes, that are not realized by group actions on closed aspherical manifolds M. These will also provide new counterexamples to the Nielsen realization problem about lifting homotopy actions of finite groups to honest group actions. Our examples show that one cannot guarantee that a given action of a finitely generated group π on Euclidean space extends to an action of , a group containing π as a subgroup of finite index, even when all the torsion of lives in π.

show abstract

“…For the computation of these terms UNil n (Z/2 * Z/2; R) we refer to [2], [9] and [10]. They have exponent four and they are either trivial or are infinitely generated as abelian groups.…”

Section: Next We Compute the Groups Hmentioning

confidence: 99%

K– andL–theory of the semi-direct product of the discrete 3–dimensional Heisenberg group by ℤ∕4

Lueck

2005

Geom. Topol.

View full text Add to dashboard Cite

We compute the group homology, the topological K -theory of the reduced C * -algebra, the algebraic K -theory and the algebraic L-theory of the group ring of the semi-direct product of the three-dimensional discrete Heisenberg group by Z/4. These computations will follow from the more general treatment of a certain class of groups G which occur as extensions 1 → K → G → Q → 1 of a torsionfree group K by a group Q which satisfies certain assumptions. The key ingredients are the Baum-Connes and Farrell-Jones Conjectures and methods from equivariant algebraic topology.

show abstract

The surgery obstruction groups of the infinite dihedral group

Cited by 21 publications

References 25 publications

The p-chain Spectral Sequence

The p-chain Spectral Sequence

On the generalized Nielsen realization problem

K– andL–theory of the semi-direct product of the discrete 3–dimensional Heisenberg group by ℤ∕4

Contact Info

Product

Resources

About