On Groups Satisfying Poincare Duality

Johnson, F. E. A.; Wall, C. T. C.

doi:10.2307/1970827

Cited by 78 publications

(30 citation statements)

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“…With the proper notion of a coarse fibration, the proof above generalizes to show that any "coarse fibration" over a good coarse PD(m) base space with good coarse PD(n) fiber is a good coarse PD(m + n) space. This implies a generalization of a theorem of Bieri [Bie72] and Johnson-Wall [JW72] saying that any extension of a PD(m) group by a PD(n) group is PD(m + n); the generalized statement replaces "PD(n) group" by "coarse PD(n) group".…”

Section: Intersect Pairwise In Rays and These Three Rays Have Infinimentioning

confidence: 96%

Quasi-actions on trees I. Bounded valence

2003

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Given a bounded valence, bushy tree T , we prove that any cobounded quasi-action of a group G on T is quasiconjugate to an action of G on another bounded valence, bushy tree T . This theorem has many applications: quasi-isometric rigidity for fundamental groups of finite, bushy graphs of coarse PD(n) groups for each fixed n; a generalization to actions on Cantor sets of Sullivan's theorem about uniformly quasiconformal actions on the 2-sphere; and a characterization of locally compact topological groups which contain a virtually free group as a cocompact lattice. Finally, we give the first examples of two finitely generated groups which are quasi-isometric and yet which cannot act on the same proper geodesic metric space, properly discontinuously and cocompactly by isometries.

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Section: Intersect Pairwise In Rays and These Three Rays Have Infinimentioning

confidence: 96%

Quasi-actions on trees I. Bounded valence

2003

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“…In fact, if K is a maximal compact subgroup of G, then G/K is diffeomorphic to some R" [7], and if T g ifc, then since T is torsion free, T \ G/K is a smooth closed manifold of type K(T, 1). Hence T is actually a Poincaré Duality group [6] of dimension n, thus verifying (¡?.l). Now if A g 'S then A is a finitely generated linear group and hence there are infinitely many primes q such that A is virtually a residually-(finite çr-group}.…”

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confidence: 76%

Fibrations of locally symmetric spaces and the failure of the Jordan-Hölder property

Johnson¹

1986

Proc. Amer. Math. Soc.

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Abstract. We construct examples of locally symmetric spaces which fibre, with both base space and fibre also locally symmetric, in two distinct ways so that neither fibre nor base of one is homeomorphic to either fibre or base of the other. The simplest example is a complex surface which fibres over a complex curve in two essentially distinct ways.In consequence, the Jordan-Holder property fails for large classes of irreducible discrete subgroups of Lie groups. 0. Introduction. Let ^ be a class of groups. Recall that by a poly-fé' filtration on a group T we mean a sequence (rr)0

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“…Extensions and amalgams. Using (2) and criteria for duality one proves There is a converse of this in the sense of [2, Theorem A] ; and there is also a "finite extension Theorem" generalizing the corresponding result in [1] and [5]. …”

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confidence: 76%