In mathematics, the chromatic spectral sequence is a
spectral sequence
In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and since their introduction by , they h ...
, introduced by , used for calculating the initial term of the
Adams spectral sequence In mathematics, the Adams spectral sequence is a spectral sequence introduced by which computes the stable homotopy groups of topological spaces. Like all spectral sequences, it is a computational tool; it relates homology theory to what is now c ...
for
Brown–Peterson cohomology In mathematics, Brown–Peterson cohomology is a generalized cohomology theory introduced by
, depending on a choice of prime ''p''. It is described in detail by .
Its representing spectrum is denoted by BP.
Complex cobordism and Quillen's idempot ...
, which is in turn used for calculating the
stable homotopy groups of spheres
In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. They are examples of topological invariants, which reflect, in algebraic terms, the structure ...
.
See also
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Chromatic homotopy theory
In mathematics, chromatic homotopy theory is a subfield of stable homotopy theory that studies complex-oriented cohomology theory, complex-oriented cohomology theories from the "chromatic" point of view, which is based on Daniel Quillen, Quillen's ...
*
Adams-Novikov spectral sequence In mathematics, the Adams spectral sequence is a spectral sequence introduced by which computes the stable homotopy groups of topological spaces. Like all spectral sequences, it is a computational tool; it relates homology theory to what is now c ...
*
p-local spectrum
References
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*
Spectral sequences
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