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- In mathematics, the Atiyah–Hirzebruch spectral sequence is a spectral sequence for calculating generalized cohomology, introduced by Michael Atiyah and Friedrich Hirzebruch in the special case of topological K-theory. For a CW complex and a generalized cohomology theory , it relates the generalized cohomology groups with 'ordinary' cohomology groups with coefficients in the generalized cohomology of a point. More precisely, the term of the spectral sequence is , and the spectral sequence converges conditionally to . 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 . It can be derived from an exact couple that gives the page of the Serre spectral sequence, except with the ordinary cohomology groups replaced with . In detail, assume to be the total space of a Serre fibration with fibre and base space . The filtration of by its -skeletons gives rise to a filtration of . There is a corresponding spectral sequence with term and converging to the associated graded ring of the filtered ring . This is the Atiyah–Hirzebruch spectral sequence in the case where the fibre is a point. (en)
- Inom matematiken är Atiyah–Hirzebruchs spektralföljd en som används för att beräkna , införd av ) i specialfallet topologisk K-teori. För ett X ger den ett samband mellan de generaliserade kohomolgigrupperna hi(X) och vanliga kohomologigrupper H j med koefficienter i den generaliserade kohomologin för en punkt. (sv)
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- 9369 (xsd:nonNegativeInteger)
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- Friedrich Hirzebruch (en)
- Michael Atiyah (en)
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- Michael (en)
- Friedrich (en)
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- Atiyah (en)
- Hirzebruch (en)
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- Inom matematiken är Atiyah–Hirzebruchs spektralföljd en som används för att beräkna , införd av ) i specialfallet topologisk K-teori. För ett X ger den ett samband mellan de generaliserade kohomolgigrupperna hi(X) och vanliga kohomologigrupper H j med koefficienter i den generaliserade kohomologin för en punkt. (sv)
- In mathematics, the Atiyah–Hirzebruch spectral sequence is a spectral sequence for calculating generalized cohomology, introduced by Michael Atiyah and Friedrich Hirzebruch in the special case of topological K-theory. For a CW complex and a generalized cohomology theory , it relates the generalized cohomology groups with 'ordinary' cohomology groups with coefficients in the generalized cohomology of a point. More precisely, the term of the spectral sequence is , and the spectral sequence converges conditionally to . and converging to the associated graded ring of the filtered ring . (en)
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- Atiyah–Hirzebruch spectral sequence (en)
- Atiyah–Hirzebruchs spektralföljd (sv)
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