See homotopy in All languages combined, or Wiktionary
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Dwyer, editor, Stable and Unstable Homotopy, American Mathematical Society, page 279:", "text": "An integer M is called an exponent for the torsion of an abelian group G if M * (torsion of G) = 0. We say that M is a homotopy exponent for a space X if M is an exponent for πₖ (X) for all k.", "type": "quote" }, { "ref": "2001, F. R. Cohen, S. Gitler, “Loop-spaces of configuration spaces, braid-like groups, and knots”, in Jaume Aguadé, Carles Broto, Carles Casacuberta, editors, Cohomological Methods in Homotopy Theory, Springer (Birkhäuser), page 63:", "text": "A graded Lie algebra arises from these maps via the Samelson product in homotopy, the so-called homotopy Lie algebra which is discussed below.", "type": "quote" }, { "text": "2010, Vladimir G. Turaev, Homotopy Quantum Field Theory, European Mathematical Society, page xi,\nIn this monograph we apply the idea of a TQFT to maps from manifolds to topological spaces. This leads us to a notion of a (d + 1)-dimensional homotopy quantum field theory (HQFT) which may be described as a TQFT for closed oriented d-dimensional manifolds and compact oriented (d + 1)-dimensional cobordisms endowed with maps to a given space X." } ], "glosses": [ "A continuous deformation of one continuous function or map to another." ], "hyponyms": [ { "_dis1": "76 13 6 3 3", "sense": "continuous deformation", "word": "isotopy" }, { "_dis1": "76 13 6 3 3", "sense": "continuous deformation", "word": "regular homotopy" } ], "id": "en-homotopy-en-noun-mk5aiw6X", "links": [ [ "topology", "topology" ], [ "continuous", "continuous" ], [ "deformation", "deformation" ], [ "continuous function", "continuous function" ], [ "map", "map" ] ], "raw_glosses": [ "(topology) A continuous deformation of one continuous function or map to another." ], "tags": [ "countable", "uncountable" ], "topics": [ "mathematics", "sciences", "topology" ], "translations": [ { "_dis1": "56 17 4 10 12", 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"sense": "(topology) continuous deformation of one continuous function to another", "word": "ホモトピー" }, { "_dis1": "56 17 4 10 12", "code": "ko", "lang": "Korean", "roman": "yeonsok byeonhyeong hamsu", "sense": "(topology) continuous deformation of one continuous function to another", "word": "연속 변형 함수" }, { "_dis1": "56 17 4 10 12", "code": "ko", "lang": "Korean", "roman": "homotopi", "sense": "(topology) continuous deformation of one continuous function to another", "word": "호모토피" }, { "_dis1": "56 17 4 10 12", "code": "fa", "lang": "Persian", "roman": "hemotopi", "sense": "(topology) continuous deformation of one continuous function to another", "word": "هموتوپی" }, { "_dis1": "56 17 4 10 12", "code": "pt", "lang": "Portuguese", "sense": "(topology) continuous deformation of one continuous function to another", "tags": [ "feminine" ], "word": "homotopia" }, { "_dis1": "56 17 4 10 12", "code": "es", "lang": "Spanish", "sense": "(topology) continuous deformation of one continuous function to another", "tags": [ "feminine" ], "word": "homotopía" }, { "_dis1": "56 17 4 10 12", "code": "uk", "lang": "Ukrainian", "roman": "homotopija", "sense": "(topology) continuous deformation of one continuous function to another", "tags": [ "feminine" ], "word": "гомотопія" }, { "_dis1": "56 17 4 10 12", "code": "vi", "lang": "Vietnamese", "sense": "(topology) continuous deformation of one continuous function to another", "word": "đồng luân" } ] }, { "categories": [], "glosses": [ "The relationship between two continuous functions where homotopy from one to the other is evident." ], "id": "en-homotopy-en-noun-YpP8NWnM", "raw_glosses": [ "(uncountable) The relationship between two continuous functions where homotopy from one to the other is evident." ], "tags": [ "uncountable" ] }, { "alt_of": [ { "extra": "the systematic study of homotopies and their equivalence classes", "word": "homotopy theory" } ], "categories": [ { "kind": "other", "name": "English links with redundant 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"parents": [], "source": "w+disamb" }, { "_dis": "8 26 44 14 8", "kind": "other", "name": "Terms with Vietnamese translations", "parents": [], "source": "w+disamb" } ], "glosses": [ "Ellipsis of homotopy theory. (the systematic study of homotopies and their equivalence classes)." ], "id": "en-homotopy-en-noun-s5Y-xV5B", "links": [ [ "homotopy theory", "homotopy theory#English" ], [ "equivalence class", "equivalence class#English" ] ], "raw_glosses": [ "(informal) Ellipsis of homotopy theory. 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