For $S_\bullet$ a spectrum, its *cylinder spectrum* $Cyl(E)_\bullet$ has as component spaces the reduced cylinder spaces over the original component spaces:

$Cyl(E)_n \coloneqq I_+ \wedge E_n
\,,$

i.e. the smash product (of pointed topological spaces) of $E_n$ with the unit inveral with a dijoint basepoint adjoined.

Cylinder spectra serve to define left homotopy of spectra as for other cylinder objects.

Early lecture notes include

- Frank Adams, part III, section 2
*Stable homotopy and generalised homology*, 1974

Last revised on April 14, 2016 at 16:07:21. See the history of this page for a list of all contributions to it.