About: Homotopy fiber

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In mathematics, especially homotopy theory, the homotopy fiber (sometimes called the mapping fiber) is part of a construction that associates a fibration to an arbitrary continuous function of topological spaces . It acts as a homotopy theoretic kernel of a mapping of topological spaces due to the fact it yields a long exact sequence of homotopy groups Moreover, the homotopy fiber can be found in other contexts, such as homological algebra, where the distinguished triangle

Attributes	Values
rdfs:label	Homotopie-Faser (de) Homotopy fiber (en)
rdfs:comment	In der Algebraischen Topologie, einem Teilgebiet der Mathematik, ist die Homotopie-Faser einer Abbildung ein nützlicher Begriff der Homotopietheorie. (de) In mathematics, especially homotopy theory, the homotopy fiber (sometimes called the mapping fiber) is part of a construction that associates a fibration to an arbitrary continuous function of topological spaces . It acts as a homotopy theoretic kernel of a mapping of topological spaces due to the fact it yields a long exact sequence of homotopy groups Moreover, the homotopy fiber can be found in other contexts, such as homological algebra, where the distinguished triangle (en)
dct:subject	Algebraic topology Homotopy theory
Wikipage page ID	19207725 (xsd:integer)
Wikipage revision ID	1051624563 (xsd:integer)
Link from a Wikipage to another Wikipage	Homotopy colimit Compact-open topology Continuous function Mathematics Quasi-fibration Homotopy cofiber Homotopy equivalent Long exact sequence Function space Mapping cone (topology) Mapping cylinder Adams resolution Topological spaces Algebraic topology Duality (mathematics) Deformation retract Homotopy theory Five Lemma Homotopy group Homotopy theory Fibration Puppe sequence Weak equivalence (homotopy theory) Mapping path space Whitehead tower Postnikov tower
Link from a Wikipage to an external page	http://www.math.cornell.edu/~hatcher/AT/ATpage.html
sameAs	Homotopy fiber Homotopy fiber Homotopy fiber Homotopy fiber Homotopy fiber
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Math dbt:Reflist
has abstract	In der Algebraischen Topologie, einem Teilgebiet der Mathematik, ist die Homotopie-Faser einer Abbildung ein nützlicher Begriff der Homotopietheorie. (de) In mathematics, especially homotopy theory, the homotopy fiber (sometimes called the mapping fiber) is part of a construction that associates a fibration to an arbitrary continuous function of topological spaces . It acts as a homotopy theoretic kernel of a mapping of topological spaces due to the fact it yields a long exact sequence of homotopy groups Moreover, the homotopy fiber can be found in other contexts, such as homological algebra, where the distinguished triangle gives a long exact sequence analogous to the long exact sequence of homotopy groups. There is a dual construction called the homotopy cofiber. (en)
gold:hypernym	Part
prov:wasDerivedFrom	wikipedia-en:Homotopy_fiber?oldid=1051624563&ns=0
page length (characters) of wiki page	9486 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Homotopy_fiber
is Link from a Wikipage to another Wikipage of	Path space fibration Homotopical connectivity Homotopy colimit and limit Obstruction theory Q-construction Glossary of algebraic topology String group Mapping cone (topology) Nilpotent space Adams resolution Locally compact abelian group Postnikov system Cofibration Homotopy group Assembly map Fibration Puppe sequence Mapping fiber Mapping fibre Homotopy fibre
is Wikipage redirect of	Mapping fiber Mapping fibre Homotopy fibre
is foaf:primaryTopic of	wikipedia-en:Homotopy_fiber

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