• mathematics, the AtiyahHirzebruch spectral sequence is a spectral sequence for calculating generalized cohomology, introduced by Michael Atiyah and Friedrich...
    9 KB (1,971 words) - 07:37, 22 July 2024
  • Thumbnail for Michael Atiyah
    The AtiyahHirzebruch spectral sequence relates the ordinary cohomology of a space to its generalized cohomology theory. (Atiyah and Hirzebruch used...
    83 KB (8,832 words) - 18:56, 18 May 2025
  • Some notable spectral sequences are: AtiyahHirzebruch spectral sequence of an extraordinary cohomology theory Bar spectral sequence for the homology...
    51 KB (10,712 words) - 03:03, 6 July 2025
  • Thumbnail for Friedrich Hirzebruch
    theorem; it was also a precursor of the Atiyah–Singer index theorem and Grothendieck's powerful generalisation. Hirzebruch's book Neue topologische Methoden in...
    13 KB (1,139 words) - 20:26, 15 February 2025
  • 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...
    9 KB (1,349 words) - 19:33, 7 January 2025
  • extraordinary (co)homology theory for a CW complex, the AtiyahHirzebruch spectral sequence is the analogue of cellular homology. Some examples: For...
    24 KB (3,603 words) - 13:33, 3 July 2025
  • existence of a spectral sequence like the AtiyahHirzebruch spectral sequence in topological K-theory. Quillen's proposed spectral sequence would start from...
    77 KB (10,647 words) - 03:27, 4 May 2025
  • spectral sequence from motivic cohomology to algebraic K-theory for every smooth scheme X over a field, analogous to the Atiyah-Hirzebruch spectral sequence...
    18 KB (2,437 words) - 22:11, 22 January 2025
  • the AtiyahHirzebruch spectral sequence, which makes it very accessible. The only required computations for understanding the spectral sequences are computing...
    27 KB (4,403 words) - 06:31, 11 May 2025
  • Thumbnail for Cobordism
    theory of a point and the homology of the space X, though the AtiyahHirzebruch spectral sequence gives a starting point for calculations. The computation...
    34 KB (5,328 words) - 19:57, 4 July 2025
  • Thumbnail for Alexander Beilinson
    related to algebraic K-theory by a motivic spectral sequence, analogous to the AtiyahHirzebruch spectral sequence in algebraic topology. These conjectures...
    11 KB (1,030 words) - 19:02, 16 June 2025
  • integers and l is prime, then there is a spectral sequence analogous to the AtiyahHirzebruch spectral sequence, starting at E 2 p q = H etale p ( Spec ...
    5 KB (534 words) - 05:21, 25 May 2025
  • Thumbnail for Victor Buchstaber
    cobordism theory. He calculated the differential in the Atiyah-Hirzebruch spectral sequence in K-theory and complex cobordism theory, constructed Chern-Dold...
    4 KB (431 words) - 12:15, 7 November 2024
  • Aspherical space assembly map Atiyah 1.  Michael Atiyah. 2.  Atiyah duality. 3.  The AtiyahHirzebruch spectral sequence. bar construction based space...
    53 KB (7,652 words) - 01:20, 30 June 2025
  • A. Field of fractions Localization Topological K-theory AtiyahHirzebruch spectral sequence for computing topological K-theory Bruns, Winfried; Gubeladze...
    24 KB (4,178 words) - 20:29, 18 May 2025
  • must quotient by these large gauge transformations. The AtiyahHirzebruch spectral sequence constructs twisted K-theory, with a twist given by the NS...
    23 KB (3,013 words) - 19:17, 21 November 2024
  • Postnikov systems to give an alternative construction of the AtiyahHirzebruch spectral sequence. With this construction, the differentials can be better...
    9 KB (930 words) - 13:50, 15 March 2025
  • and social sciences, a grouping of academic disciplines AtiyahHirzebruch spectral sequence, computational tool from homological algebra American Heinrich...
    794 bytes (122 words) - 08:38, 11 December 2024
  • {\displaystyle {H_{2k+1}}(\mathbb {CP} ^{n};\mathbb {Z} )=0.} The AtiyahHirzebruch spectral sequence is the analogous method of computing the (co)homology of...
    15 KB (3,471 words) - 17:50, 18 May 2025
  • Thumbnail for Massey product
    twisted K-theory by means of the AtiyahHirzebruch spectral sequence (AHSS). In particular, if H is the twist 3-class, Atiyah & Segal (2006) showed that, rationally...
    12 KB (1,885 words) - 14:47, 26 May 2025
  • Thumbnail for Fields Medal
    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)...
    90 KB (4,942 words) - 13:45, 26 June 2025
  • 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...
    29 KB (4,373 words) - 01:23, 1 April 2025
  • Thumbnail for Algebraic topology
    algebra Homological algebra K-theory Lie algebroid Lie groupoid Serre spectral sequence Sheaf Topological quantum field theory Fraleigh (1976, p. 163) Fréchet...
    19 KB (2,093 words) - 21:19, 12 June 2025
  • Thumbnail for Ramond–Ramond field
    classes. These correspond to the cohomology classes in the Atiyah Hirzebruch Spectral Sequence construction of twisted K-theory, which are only defined...
    15 KB (2,285 words) - 11:50, 11 August 2024
  • Physicist typically want to calculate twisted K-theory using the AtiyahHirzebruch spectral sequence. The idea is that one begins with all of the even or all...
    12 KB (1,905 words) - 12:45, 17 March 2025
  • {\displaystyle E} is complex-orientable. This follows from the AtiyahHirzebruch spectral sequence. Examples: An ordinary cohomology with any coefficient ring...
    3 KB (496 words) - 07:19, 24 June 2025
  • 2016-03-18. Atiyah, Michael (2000). "The geometry of classical particles". In Yau, Shing-Tung (ed.). Papers dedicated to Atiyah, Bott, Hirzebruch, and Singer...
    195 KB (20,069 words) - 08:05, 26 June 2025
  • topology) Atiyah–Bott fixed-point theorem (differential topology) Bing's recognition theorem (geometric topology) Birman short exact sequence (geometric...
    78 KB (6,296 words) - 20:31, 6 July 2025