Classifying Spaces and Fibrations

E777845

mathematical work research monograph

"Classifying Spaces and Fibrations" is a mathematical work that develops the theory of classifying spaces in algebraic topology and their relationship to fiber bundles and fibrations.

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Label	Occurrences
Classifying Spaces and Fibrations canonical	1

Statements (45)

Predicate	Object
instanceOf	mathematical work ⓘ research monograph ⓘ
aim	to develop the theory of classifying spaces in connection with fibrations ⓘ to provide homotopy-theoretic tools for classifying bundles and fibrations ⓘ
area	pure mathematics ⓘ
concerns	classification of certain fibrations up to fiber homotopy equivalence ⓘ classification of principal bundles by homotopy classes of maps into BG ⓘ construction of universal fibrations ⓘ relationship between cohomology and characteristic classes of bundles ⓘ
describes	conditions under which a fibration is classified by a map into a classifying space ⓘ how isomorphism classes of bundles correspond to homotopy classes of maps into a classifying space ⓘ universal fibrations whose pullbacks give all fibrations of a given type ⓘ
field	algebraic topology ⓘ
intendedFor	graduate students in topology ⓘ researchers in algebraic topology ⓘ
relates	classifying spaces ⓘ fiber bundles ⓘ fibrations ⓘ
studies	spaces that classify fibrations up to equivalence ⓘ spaces that classify isomorphism classes of bundles ⓘ
subfield	homotopy theory ⓘ topology ⓘ
topic	Serre fibrations NERFINISHED ⓘ classifying space BG of a topological group G ⓘ classifying spaces ⓘ cohomological invariants of bundles ⓘ construction of classifying spaces ⓘ fiber bundles ⓘ fibrations ⓘ homotopy classification of bundles ⓘ homotopy equivalence and classification ⓘ homotopy lifting properties ⓘ homotopy theory ⓘ mapping spaces into classifying spaces ⓘ principal bundles ⓘ relationship between fibrations and homotopy groups ⓘ structure of fiber bundles via classifying maps ⓘ universal bundles ⓘ universal properties of classifying spaces ⓘ
usesConcept	classifying map ⓘ fiber homotopy equivalence ⓘ homotopy lifting property ⓘ principal G-bundle ⓘ topological group ⓘ universal bundle construction ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Ieke Moerdijk → notableWork → Classifying Spaces and Fibrations ⓘ