Loterre: Mathematics: Margulis lemma

geometry > differential geometry > Riemannian geometry > Margulis lemma

geometry > non-Euclidean geometry > hyperbolic geometry > Margulis lemma

Margulis lemma

In differential geometry, the Margulis lemma (named after Grigory Margulis) is a result about discrete subgroups of isometries of a non-positively curved Riemannian manifold (e.g. the hyperbolic n-space). Roughly, it states that within a fixed radius, usually called the Margulis constant, the structure of the orbits of such a group cannot be too complicated. More precisely, within this radius around a point all points in its orbit are in fact in the orbit of a nilpotent subgroup (in fact a bounded finite number of such).
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Margulis_lemma)

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