About: Path space fibration

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In algebraic topology, the path space fibration over a based space is a fibration of the form where * is the path space of X; i.e., equipped with the compact-open topology. * is the fiber of over the base point of X; thus it is the loop space of X. The space consists of all maps from I to X that may not preserve the base points; it is called the free path space of X and the fibration given by, say, , is called the free path space fibration.

Attributes	Values
rdfs:label	Path space fibration (en)
rdfs:comment	In algebraic topology, the path space fibration over a based space is a fibration of the form where * is the path space of X; i.e., equipped with the compact-open topology. * is the fiber of over the base point of X; thus it is the loop space of X. The space consists of all maps from I to X that may not preserve the base points; it is called the free path space of X and the fibration given by, say, , is called the free path space fibration. (en)
dcterms:subject	Algebraic topology Homotopy theory
Wikipage page ID	48842115 (xsd:integer)
Wikipage revision ID	1104064511 (xsd:integer)
Link from a Wikipage to another Wikipage	Path space (algebraic topology) Algebraic topology Homotopy equivalence Compact-open topology Monoid action Operad Mapping cone (topology) G-fibration American Mathematical Society Algebraic topology Graduate Texts in Mathematics Homotopy theory Interval (mathematics) John Moore Homotopy Homotopy fiber Springer Science+Business Media Fiber-homotopy equivalence Fibration Associative Category (mathematics) Unit interval Loop space University of Chicago Press Topological monoid Based space
Link from a Wikipage to an external page	http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf http://www.maths.ed.ac.uk/~aar/papers/davkir.pdf%7Ctitle= https://books.google.com/books%3Fid=wlrvAAAAMAAJ%7Cedition=3rd%7Cseries=
sameAs	Path space fibration Path space fibration
dbp:wikiPageUsesTemplate	dbt:' dbt:Cite_book dbt:Clarify dbt:Reflist
has abstract	In algebraic topology, the path space fibration over a based space is a fibration of the form where * is the path space of X; i.e., equipped with the compact-open topology. * is the fiber of over the base point of X; thus it is the loop space of X. The space consists of all maps from I to X that may not preserve the base points; it is called the free path space of X and the fibration given by, say, , is called the free path space fibration. The path space fibration can be understood to be dual to the mapping cone. The reduced fibration is called the mapping fiber or, equivalently, the homotopy fiber. (en)
prov:wasDerivedFrom	wikipedia-en:Path_space_fibration?oldid=1104064511&ns=0
page length (characters) of wiki page	8228 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Path_space_fibration
is Link from a Wikipage to another Wikipage of	Path space (algebraic topology) Glossary of algebraic topology Leray spectral sequence Path space Cofibration Fibration Serre spectral sequence Free path space Mapping path space Path fibration Moore's path space fibration Moore path Moore path space
is Wikipage redirect of	Free path space Mapping path space Path fibration Moore's path space fibration Moore path Moore path space
is foaf:primaryTopic of	wikipedia-en:Path_space_fibration

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