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On poénaru's inverse-representations
Abstract
The present survey deals with the notion of topological inverse-representation
for spaces and groups, a concept introduced by Valentin Poenaru in the 80's,
and largely used in successive works in geometric topology. We recall the origin of
this concept as a low-dimensional topology tool for studying compact 3-manifolds
and their universal covering spaces. We also illustrate some recent developments in
geometric group theory.
Key words: 3-manifolds, discrete groups, singularities, simple connectivity at innity,
geometric simple connectivity, qsf-property.
for spaces and groups, a concept introduced by Valentin Poenaru in the 80's,
and largely used in successive works in geometric topology. We recall the origin of
this concept as a low-dimensional topology tool for studying compact 3-manifolds
and their universal covering spaces. We also illustrate some recent developments in
geometric group theory.
Key words: 3-manifolds, discrete groups, singularities, simple connectivity at innity,
geometric simple connectivity, qsf-property.
