A homotopy cofiber of a based map is the homotopy pushout of . For spaces it can be modeled by the mapping cone, obtained by attaching the cone on to using . For spectra, a cofiber sequence extends to and induces a long exact sequence of homotopy groups. The cofiber of multiplication by on the sphere spectrum is the mod- Moore spectrum. Successive cofibers specify the pieces of a filtration, while the attaching maps record whether those pieces split.

See also

Mapping Cone, Sphere Spectrum, Thick Subcategory, Topological Spectrum

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References

May, J. P. A Concise Course in Algebraic Topology. Chicago, IL: University of Chicago Press, 1999.

Cite this as:

Weisstein, Eric W. "Cofiber." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Cofiber.html

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