mathematics, the Atiyah–Hirzebruch spectral sequence is a spectral sequence for calculating generalized cohomology, introduced by Michael Atiyah and Friedrich...

The Atiyah–Hirzebruch spectral sequence relates the ordinary cohomology of a space to its generalized cohomology theory. (Atiyah and Hirzebruch used...

Some notable spectral sequences are: Atiyah–Hirzebruch spectral sequence of an extraordinary cohomology theory Bar spectral sequence for the homology...

theorem; it was also a precursor of the Atiyah–Singer index theorem and Grothendieck's powerful generalisation. Hirzebruch's book Neue topologische Methoden in...

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...

extraordinary (co)homology theory for a CW complex, the Atiyah–Hirzebruch spectral sequence is the analogue of cellular homology. Some examples: For...

existence of a spectral sequence like the Atiyah–Hirzebruch spectral sequence in topological K-theory. Quillen's proposed spectral sequence would start from...

spectral sequence from motivic cohomology to algebraic K-theory for every smooth scheme X over a field, analogous to the Atiyah-Hirzebruch spectral sequence...

the Atiyah–Hirzebruch spectral sequence, which makes it very accessible. The only required computations for understanding the spectral sequences are computing...

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...

related to algebraic K-theory by a motivic spectral sequence, analogous to the Atiyah–Hirzebruch spectral sequence in algebraic topology. These conjectures...

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 ...

cobordism theory. He calculated the differential in the Atiyah-Hirzebruch spectral sequence in K-theory and complex cobordism theory, constructed Chern-Dold...

Aspherical space assembly map Atiyah 1.  Michael Atiyah. 2.  Atiyah duality. 3.  The Atiyah–Hirzebruch spectral sequence. bar construction based space...

A. Field of fractions Localization Topological K-theory Atiyah–Hirzebruch spectral sequence for computing topological K-theory Bruns, Winfried; Gubeladze...

must quotient by these large gauge transformations. The Atiyah–Hirzebruch spectral sequence constructs twisted K-theory, with a twist given by the NS...

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...

{\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...

Postnikov systems to give an alternative construction of the Atiyah–Hirzebruch spectral sequence. With this construction, the differentials can be better...

and social sciences, a grouping of academic disciplines Atiyah–Hirzebruch spectral sequence, computational tool from homological algebra American Heinrich...

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)...

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...

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...

algebra Homological algebra K-theory Lie algebroid Lie groupoid Serre spectral sequence Sheaf Topological quantum field theory Fraleigh (1976, p. 163) Fréchet...

classes. These correspond to the cohomology classes in the Atiyah Hirzebruch Spectral Sequence construction of twisted K-theory, which are only defined...

{\displaystyle E} is complex-orientable. This follows from the Atiyah–Hirzebruch spectral sequence. Examples: An ordinary cohomology with any coefficient ring...

2016-03-18. Atiyah, Michael (2000). "The geometry of classical particles". In Yau, Shing-Tung (ed.). Papers dedicated to Atiyah, Bott, Hirzebruch, and Singer...

topology) Atiyah–Bott fixed-point theorem (differential topology) Bing's recognition theorem (geometric topology) Birman short exact sequence (geometric...