The QSF property for groups and spaces

Brick, Stephen G.

doi:10.1007/bf02572610

Cited by 40 publications

(58 citation statements)

References 10 publications

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“…An example comes from an asymptotic invariant of discrete groups (i.e. a well-defined property of groups which is invariant under quasi-isometries [8,13]) of topological nature, due to Brick and Mihalik [2,18]. Definition 2.8 (See [2,18]).…”

Section: Resultsmentioning

confidence: 99%

“…a well-defined property of groups which is invariant under quasi-isometries [8,13]) of topological nature, due to Brick and Mihalik [2,18]. Definition 2.8 (See [2,18]). The simply connected non-compact complex X is qsf (i.e., quasi simply filtered ) if for any connected finite subcomplex C ⊂ X there exists a finite simply connected complex K and a cellular map f : K → X so that C ⊂ f (K) and f | f −1 (C) : f −1 (C) → C is a cellular homeomorphism.…”

Section: Resultsmentioning

confidence: 99%

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Some Algebraic and Topological Properties of the Nonabelian Tensor Product

Otera¹,

Russo²,

Tanasi³

2013

Bulletin of the Korean Mathematical Society

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Some Algebraic and Topological Properties of the Nonabelian Tensor Product

Otera¹,

Russo²,

Tanasi³

2013

Bulletin of the Korean Mathematical Society

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“…It was shown in [2] that all one-relator groups are QSF. Furthermore, the properties QSF and WGSC have recently been shown to be equivalent (see [15,16]).…”

Section: One-relator Groups and Their Structure At Infinitymentioning

confidence: 99%

One-relator groups and proper 3-realizability

Cárdenas¹,

Lasheras²,

Quintero³

et al. 2009

Rev. Mat. Iberoam.

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How different is the universal cover of a given finite 2-complex from a 3-manifold (from the proper homotopy viewpoint)? Regarding this question, we recall that a finitely presented group G is said to be properly 3-realizable if there exists a compact 2-polyhedron K with π 1 (K) ∼ = G whose universal coverK has the proper homotopy type of a PL 3-manifold (with boundary). In this paper, we study the asymptotic behavior of finitely generated one-relator groups and show that those having finitely many ends are properly 3-realizable, by describing what the fundamental pro-group looks like, showing a property of one-relator groups which is stronger than the QSF property of Brick (from the proper homotopy viewpoint) and giving an alternative proof of the fact that one-relator groups are semistable at infinity.

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“…If G has a tame combing, then G is quasi-simply-filtrated (see [BM1]) by Theorem 3 of [MT]. We thus have the following generalization of the main theorem of [BM2].…”

Section: Introductionmentioning

confidence: 96%

Group extensions and tame pairs

Mihalik

1999

Trans. Amer. Math. Soc.

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Abstract. Tame pairs of groups were introduced to study the missing boundary problem for covers of compact 3-manifolds. In this paper we prove that if 1 → A → G → B → 1 is an exact sequence of infinite finitely presented groups or if G is an ascending HNN-extension with base A and H is a certain type of finitely presented subgroup of A, then the pair (G, H) is tame.Also we develop a technique for showing certain groups cannot be the fundamental group of a compact 3-manifold. In particular, we give an elementary proof of the result of R. Bieri, W. Neumann and R. Strebel:A strictly ascending HNN-extension cannot be the fundamental group of a compact 3-manifold.

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The QSF property for groups and spaces

Cited by 40 publications

References 10 publications

Some Algebraic and Topological Properties of the Nonabelian Tensor Product

Some Algebraic and Topological Properties of the Nonabelian Tensor Product

One-relator groups and proper 3-realizability

Group extensions and tame pairs

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