mathematics, the Atiyah–Hirzebruch spectral sequence is a spectral sequence for calculating generalized cohomology, introduced by Michael Atiyah and Friedrich...
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The Atiyah–Hirzebruch spectral sequence relates the ordinary cohomology of a space to its generalized cohomology theory. (Atiyah and Hirzebruch used...
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Some notable spectral sequences are: Atiyah–Hirzebruch spectral sequence of an extraordinary cohomology theory Bar spectral sequence for the homology...
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theorem; it was also a precursor of the Atiyah–Singer index theorem and Grothendieck's powerful generalisation. Hirzebruch's book Neue topologische Methoden in...
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bundle E over X. This holds whenever E is a spin-bundle. The Atiyah-Hirzebruch spectral sequence allows computation of K-groups from ordinary cohomology groups...
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extraordinary (co)homology theory for a CW complex, the Atiyah–Hirzebruch spectral sequence is the analogue of cellular homology. Some examples: For...
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Algebraic K-theory (section Long exact sequences)
existence of a spectral sequence like the Atiyah–Hirzebruch spectral sequence in topological K-theory. Quillen's proposed spectral sequence would start from...
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spectral sequence from motivic cohomology to algebraic K-theory for every smooth scheme X over a field, analogous to the Atiyah-Hirzebruch spectral sequence...
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the Atiyah–Hirzebruch spectral sequence, which makes it very accessible. The only required computations for understanding the spectral sequences are computing...
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theory of a point and the homology of the space X, though the Atiyah–Hirzebruch spectral sequence gives a starting point for calculations. The computation...
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related to algebraic K-theory by a motivic spectral sequence, analogous to the Atiyah–Hirzebruch spectral sequence in algebraic topology. These conjectures...
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integers and l is prime, then there is a spectral sequence analogous to the Atiyah–Hirzebruch spectral sequence, starting at E 2 p q = H etale p ( Spec ...
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cobordism theory. He calculated the differential in the Atiyah-Hirzebruch spectral sequence in K-theory and complex cobordism theory, constructed Chern-Dold...
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Aspherical space assembly map Atiyah 1. Michael Atiyah. 2. Atiyah duality. 3. The Atiyah–Hirzebruch spectral sequence. bar construction based space...
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A. Field of fractions Localization Topological K-theory Atiyah–Hirzebruch spectral sequence for computing topological K-theory Bruns, Winfried; Gubeladze...
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must quotient by these large gauge transformations. The Atiyah–Hirzebruch spectral sequence constructs twisted K-theory, with a twist given by the NS...
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Postnikov systems to give an alternative construction of the Atiyah–Hirzebruch spectral sequence. With this construction, the differentials can be better...
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and social sciences, a grouping of academic disciplines Atiyah–Hirzebruch spectral sequence, computational tool from homological algebra American Heinrich...
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{\displaystyle {H_{2k+1}}(\mathbb {CP} ^{n};\mathbb {Z} )=0.} The Atiyah–Hirzebruch spectral sequence is the analogous method of computing the (co)homology of...
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twisted K-theory by means of the Atiyah–Hirzebruch spectral sequence (AHSS). In particular, if H is the twist 3-class, Atiyah & Segal (2006) showed that, rationally...
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the original on 30 August 2014. Retrieved 17 August 2014. "Sir Michael F. Atiyah : The Abel Prize" (PDF). Upcommons.upc.edu (in Spanish). Archived (PDF)...
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general an integer. This was originally proven by Hirzebruch and Borel, and can be proven by the Atiyah–Singer index theorem, by realizing the  genus as...
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algebra Homological algebra K-theory Lie algebroid Lie groupoid Serre spectral sequence Sheaf Topological quantum field theory Fraleigh (1976, p. 163) Fréchet...
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classes. These correspond to the cohomology classes in the Atiyah Hirzebruch Spectral Sequence construction of twisted K-theory, which are only defined...
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Physicist typically want to calculate twisted K-theory using the Atiyah–Hirzebruch spectral sequence. The idea is that one begins with all of the even or all...
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{\displaystyle E} is complex-orientable. This follows from the Atiyah–Hirzebruch spectral sequence. Examples: An ordinary cohomology with any coefficient ring...
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2016-03-18. Atiyah, Michael (2000). "The geometry of classical particles". In Yau, Shing-Tung (ed.). Papers dedicated to Atiyah, Bott, Hirzebruch, and Singer...
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topology) Atiyah–Bott fixed-point theorem (differential topology) Bing's recognition theorem (geometric topology) Birman short exact sequence (geometric...
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