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A Generalization of the Atiyah–Hirzebruch Spectral Sequence (1997)

Hakim-Hashemi, Mehdi ; Kahn, Donald W.

Springer

K-Theory 11 (1997), S. 241-257

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ISSN: 1573-0514

Keywords: homology theory ; spectral sequence ; symmetric product

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The classical Atiyah‐Hirzebruch spectral sequence relates the ordinary homology with coefficients in h_*(*) to h*(-). We study a spectral sequence converging to h*(F(-)) where F is a (reasonable) functor on spaces. We determine precisely when this spectral sequence collapses and we develop the basic elementary theory of such functors. When F is a reduced homotopy exact functor, H*(F(-)) is a homology theory and this reduces to the classical case of Atiyah–Hirzebruch. We calculate various examples to show that the theory is nontrivial.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1007781928192

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