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- Complex-oriented_cohomology_theory abstract "In algebraic topology, a complex-orientable cohomology theory is a multiplicative cohomology theory E such that the restriction map is surjective. An element of that restricts to the canonical generator of the reduced theory is called a complex orientation. The notion is central to Quillen's work relating cohomology to formal group laws.[citation needed]If , then E is complex-orientable.Examples:An ordinary cohomology with any coefficient ring R is complex orientable, as .A complex K-theory, denoted by K, is complex-orientable, as (Bott periodicity theorem)Complex cobordism, whose spectrum is denoted by MU, is complex-orientable.A complex orientation, call it t, gives rise to a formal group law as follows: let m be the multiplicationwhere denotes a line passing through x in the underlying vector space of . Viewing,let be the pullback of t along m. It lives inand one can show it is a formal group law (e.g., satisfies associativity).".
- Complex-oriented_cohomology_theory wikiPageExternalLink coctalos.pdf.
- Complex-oriented_cohomology_theory wikiPageExternalLink 252x.html.
- Complex-oriented_cohomology_theory wikiPageID "40770350".
- Complex-oriented_cohomology_theory wikiPageRevisionID "602638823".
- Complex-oriented_cohomology_theory subject Category:Algebraic_topology.
- Complex-oriented_cohomology_theory subject Category:Cohomology_theories.
- Complex-oriented_cohomology_theory comment "In algebraic topology, a complex-orientable cohomology theory is a multiplicative cohomology theory E such that the restriction map is surjective. An element of that restricts to the canonical generator of the reduced theory is called a complex orientation.".
- Complex-oriented_cohomology_theory label "Complex-oriented cohomology theory".
- Complex-oriented_cohomology_theory sameAs m.0y7tw28.
- Complex-oriented_cohomology_theory sameAs Q16950707.
- Complex-oriented_cohomology_theory sameAs Q16950707.
- Complex-oriented_cohomology_theory wasDerivedFrom Complex-oriented_cohomology_theory?oldid=602638823.
- Complex-oriented_cohomology_theory isPrimaryTopicOf Complex-oriented_cohomology_theory.