See Margulis lemma on Wiktionary
{ "etymology_text": "Named after Grigory Margulis.", "forms": [ { "form": "the Margulis lemma", "tags": [ "canonical" ] } ], "head_templates": [ { "args": { "def": "1" }, "expansion": "the Margulis lemma", "name": "en-prop" } ], "lang": "English", "lang_code": "en", "pos": "name", "senses": [ { "categories": [ { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Differential geometry", "orig": "en:Differential geometry", "parents": [ "Geometry", "Mathematical analysis", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "A result about discrete subgroups of isometries of a non-positively curved Riemannian manifold, stating roughly that, within a fixed radius (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)." ], "id": "en-Margulis_lemma-en-name-FMr~8rA0", "links": [ [ "differential geometry", "differential geometry" ], [ "result", "result" ], [ "discrete", "discrete" ], [ "subgroup", "subgroup" ], [ "isometries", "isometry" ], [ "Riemannian manifold", "Riemannian manifold" ], [ "radius", "radius" ], [ "Margulis constant", "Margulis constant" ], [ "structure", "structure" ], [ "orbit", "orbit" ], [ "point", "point" ], [ "nilpotent", "nilpotent" ] ], "qualifier": "differential geometry", "raw_glosses": [ "(differential geometry) A result about discrete subgroups of isometries of a non-positively curved Riemannian manifold, stating roughly that, within a fixed radius (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": [ "Grigory Margulis" ] } ], "word": "Margulis lemma" }
{ "etymology_text": "Named after Grigory Margulis.", "forms": [ { "form": "the Margulis lemma", "tags": [ "canonical" ] } ], "head_templates": [ { "args": { "def": "1" }, "expansion": "the Margulis lemma", "name": "en-prop" } ], "lang": "English", "lang_code": "en", "pos": "name", "senses": [ { "categories": [ "English entries with incorrect language header", "English eponyms", "English lemmas", "English multiword terms", "English proper nouns", "English uncountable nouns", "Pages with 1 entry", "Pages with entries", "en:Differential geometry" ], "glosses": [ "A result about discrete subgroups of isometries of a non-positively curved Riemannian manifold, stating roughly that, within a fixed radius (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)." ], "links": [ [ "differential geometry", "differential geometry" ], [ "result", "result" ], [ "discrete", "discrete" ], [ "subgroup", "subgroup" ], [ "isometries", "isometry" ], [ "Riemannian manifold", "Riemannian manifold" ], [ "radius", "radius" ], [ "Margulis constant", "Margulis constant" ], [ "structure", "structure" ], [ "orbit", "orbit" ], [ "point", "point" ], [ "nilpotent", "nilpotent" ] ], "qualifier": "differential geometry", "raw_glosses": [ "(differential geometry) A result about discrete subgroups of isometries of a non-positively curved Riemannian manifold, stating roughly that, within a fixed radius (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": [ "Grigory Margulis" ] } ], "word": "Margulis lemma" }
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-04 from the enwiktionary dump dated 2024-10-02 using wiktextract (d6bf104 and a5af179). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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