About: Equivariant topology

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In mathematics, equivariant topology is the study of topological spaces that possess certain symmetries. In studying topological spaces, one often considers continuous maps , and while equivariant topology also considers such maps, there is the additional constraint that each map "respects symmetry" in both its domain and target space.

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rdfs:label	Equivariant topology (en)
rdfs:comment	In mathematics, equivariant topology is the study of topological spaces that possess certain symmetries. In studying topological spaces, one often considers continuous maps , and while equivariant topology also considers such maps, there is the additional constraint that each map "respects symmetry" in both its domain and target space. (en)
dcterms:subject	Topological spaces Topology Group actions (mathematics)
Wikipage page ID	41144410 (xsd:integer)
Wikipage revision ID	1084951106 (xsd:integer)
Link from a Wikipage to another Wikipage	Vector space Stiefel–Whitney class Mathematics Equivariant cohomology Equivariant map Equivariant stable homotopy theory Topological spaces Topology Domain of a function G-spectrum Topology Even and odd functions Discrete geometry Group (mathematics) Group action Group action (mathematics) Ham sandwich theorem Abstract algebra Codomain Borsuk–Ulam theorem Group actions (mathematics) Continuous function (topology) Principal bundle Topological space
sameAs	Equivariant topology Equivariant topology Equivariant topology Equivariant topology
dbp:wikiPageUsesTemplate	dbt:More_citations_needed dbt:Reflist dbt:Short_description
has abstract	In mathematics, equivariant topology is the study of topological spaces that possess certain symmetries. In studying topological spaces, one often considers continuous maps , and while equivariant topology also considers such maps, there is the additional constraint that each map "respects symmetry" in both its domain and target space. The notion of symmetry is usually captured by considering a group action of a group on and and requiring that is equivariant under this action, so that for all , a property usually denoted by . Heuristically speaking, standard topology views two spaces as equivalent "up to deformation," while equivariant topology considers spaces equivalent up to deformation so long as it pays attention to any symmetry possessed by both spaces. A famous theorem of equivariant topology is the Borsuk–Ulam theorem, which asserts that every -equivariant map necessarily vanishes. (en)
gold:hypernym	Study
prov:wasDerivedFrom	wikipedia-en:Equivariant_topology?oldid=1084951106&ns=0
page length (characters) of wiki page	5749 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Equivariant_topology
is Link from a Wikipage to another Wikipage of	Mary Mulry Geometric invariant theory Equivariant map Equivariant stable homotopy theory Topology Ham sandwich theorem Using the Borsuk–Ulam Theorem Equivariant algebraic topoloy
is Wikipage redirect of	Equivariant algebraic topoloy
is foaf:primaryTopic of	wikipedia-en:Equivariant_topology

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