On the fundamental groups of trees of manifolds

Fischer, Hanspeter; Guilbault, Craig R.

doi:10.2140/pjm.2005.221.49

Cited by 22 publications

(21 citation statements)

References 21 publications

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“…This homomorphism is often injective. For example, it is injective for one-dimensional spaces [15], for subsets of surfaces [19] and for certain trees of manifolds [18]. Hence, for such X, we have π s (X, x) = 1.…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

Cotorsion-free groups from a topological viewpoint

Eda

Fischer

2016

Topology and its Applications

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Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

Cotorsion-free groups from a topological viewpoint

Eda

Fischer

2016

Topology and its Applications

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“…Consequently, the fundamental group of any 1-dimensional (metric) continuum is isomorphic to a subgroup of the limit of an inverse sequence of finitely generated free groups; a fact already proved in [6] and also in [1,Theorem 5.11]. Injectivity of the above homomorphism has also been established for certain fractal-like trees of manifolds, which need not be semilocally simply connected at any point [10].…”

Section: Introductionmentioning

confidence: 83%

The fundamental groups of subsets of closed surfaces inject into their first shape groups

Fischer

Zastrow

2005

Algebr. Geom. Topol.

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We show that for every subset X of a closed surface M 2 and every x 0 ∈ X , the natural homomorphism ϕ : π 1 (X, x 0 ) →π 1 (X, x 0 ), from the fundamental group to the first shape homotopy group, is injective. In particular, if X M 2 is a proper compact subset, then π 1 (X, x 0 ) is isomorphic to a subgroup of the limit of an inverse sequence of finitely generated free groups; it is therefore locally free, fully residually free and residually finite.

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“…In this section we recall from [12] Jakobsche's definition of a family of spaces that we call (after Fischer and Guilbault [10]) trees of manifolds. We include an extension to the case of non-orientable manifolds due to P. Stallings [21].…”

Section: Trees Of Manifoldsmentioning

confidence: 99%

“…These are some of the trees of manifolds (named so in [10]) introduced by Jakobsche in [12]. Apart from being connected, these spaces are homogeneous, and thus have no local cut points.…”

Section: Introductionmentioning

confidence: 99%

Flag-no-square triangulations and Gromov boundaries in dimension 3

Przytycki¹,

Świątkowski²

2009

Groups Geom. Dyn.

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Abstract.We describe an infinite family of 3-dimensional topological spaces, which are homeomorphic to boundaries of certain word-hyperbolic groups. The groups are right-angled hyperbolic Coxeter groups, whose nerves are flag-no-square triangulations of 3-dimensional manifolds. We prove that any 3-dimensional polyhedral complex (in particular, any 3-manifold) can be triangulated in a flag-no-square way.

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On the fundamental groups of trees of manifolds

Cited by 22 publications

References 21 publications

Cotorsion-free groups from a topological viewpoint

Cotorsion-free groups from a topological viewpoint

The fundamental groups of subsets of closed surfaces inject into their first shape groups

Flag-no-square triangulations and Gromov boundaries in dimension 3

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