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- Atiyah–Hirzebruch_spectral_sequence abstract "In mathematics, the Atiyah–Hirzebruch spectral sequence is a spectral sequence for calculating generalized cohomology, introduced by Atiyah & Hirzebruch (1961) in the special case of topological K-theory. For a CW complex X, it relates the generalized cohomology groups hi(X)with 'ordinary' cohomology groups H j with coefficients in the generalized cohomology of a point. More precisely, the E2 term of the spectral sequence is Hi(X,hj(point)), and the spectral sequence converges conditionally to hi+j(X). Atiyah and Hirzebruch pointed out a generalization of their spectral sequence that also generalizes the Serre spectral sequence, and reduces to it in the case where h=H. It can be derived from an exact couple that gives the E1 page of the Serre spectral sequence, except with the ordinary cohomology groups replaced with h. In detail, assume X to be the total space of a Serre fibration with fibre F and base space B. The filtration of B by its n-skeletons gives rise to a filtration of X. There is a corresponding spectral sequence with E2 term Hp(B;h q(F))and abutting to the associated graded ring of the filtered ring hp + q(X).This is the Atiyah–Hirzebruch spectral sequence in the case where the fibre F is a point.".
- Atiyah–Hirzebruch_spectral_sequence wikiPageExternalLink books?id=4hE7AAAAIAAJ&pg=PA197.
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- Atiyah–Hirzebruch_spectral_sequence wikiPageOutDegree "16".
- Atiyah–Hirzebruch_spectral_sequence wikiPageRevisionID "556123334".
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink American_Mathematical_Society.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink CW_complex.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Category:K-theory.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Category:Spectral_sequences.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Cohomology.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Cohomology_group.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Fibration.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Filtered_algebra.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Filtration_(algebra).
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Filtration_(mathematics).
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Generalized_cohomology.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Mathematics.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink N-skeleton.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Serre_fibration.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Serre_spectral_sequence.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Spectral_sequence.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLink Topological_K-theory.
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLinkText "Atiyah–Hirzebruch spectral sequence".
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLinkText "Atiyah-Hirzebruch spectral sequence".
- Atiyah–Hirzebruch_spectral_sequence wikiPageWikiLinkText "Atiyah–Hirzebruch spectral sequence".
- Atiyah–Hirzebruch_spectral_sequence hasPhotoCollection Atiyah–Hirzebruch_spectral_sequence.
- Atiyah–Hirzebruch_spectral_sequence wikiPageUsesTemplate Template:Citation.
- Atiyah–Hirzebruch_spectral_sequence wikiPageUsesTemplate Template:Harvtxt.
- Atiyah–Hirzebruch_spectral_sequence subject Category:K-theory.
- Atiyah–Hirzebruch_spectral_sequence subject Category:Spectral_sequences.
- Atiyah–Hirzebruch_spectral_sequence comment "In mathematics, the Atiyah–Hirzebruch spectral sequence is a spectral sequence for calculating generalized cohomology, introduced by Atiyah & Hirzebruch (1961) in the special case of topological K-theory. For a CW complex X, it relates the generalized cohomology groups hi(X)with 'ordinary' cohomology groups H j with coefficients in the generalized cohomology of a point.".
- Atiyah–Hirzebruch_spectral_sequence label "Atiyah–Hirzebruch spectral sequence".
- Atiyah–Hirzebruch_spectral_sequence sameAs m.0gp9qs.
- Atiyah–Hirzebruch_spectral_sequence sameAs Atiyah–Hirzebruchs_spektralföljd.
- Atiyah–Hirzebruch_spectral_sequence sameAs Q17004665.
- Atiyah–Hirzebruch_spectral_sequence sameAs Q17004665.
- Atiyah–Hirzebruch_spectral_sequence wasDerivedFrom Atiyah–Hirzebruch_spectral_sequence?oldid=556123334.
- Atiyah–Hirzebruch_spectral_sequence isPrimaryTopicOf Atiyah–Hirzebruch_spectral_sequence.