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Home > Spectrum (homotopy theory)

In mathematics, a spectrum in homotopy theory is an object in a category constructed for the purposes of stable homotopy theory , starting with the category of CW complexes and aiming to make the suspension functor S invertible. This construction is originally due to J. M. Boardman .

The objects of the category of spectra are sequences

E_n

of CW complexes as pointed space s, such that

SE_n

is homeomorphic to a subcomplex of E_{n + 1.}

Morphisms in the category of spectra are defined in a non-obvious way, as a type of partial function, subject to an equivalence relation: essentially from the minimum mapping information that is possible, allowing S to be applied to bring any given cell into the domain.

The construction is related, on a conceptual level at least, to that of the derived category, but using spaces rather than algebra.

Homotopy theory

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Topics: Spectrum (homotopy Theory), Spectrum Of A Ring, Spectrum Of An...

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Spectrum (homotopy theory)	Spectrum (disambiguation)	Spectrum (band)
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