The smash product of based spaces 
and 
is the quotient
 |
where the wedge is the union of 
and 
. For example, 
is homeomorphic to 
. The derived smash product of spectra
extends this operation to stable homotopy theory
and has the sphere spectrum as its unit. For a
spectrum 
, generalized homology is 
. In a localized category the tensor product
may require localization after the smash product.
Complex cobordism can detect stable vanishing after taking large smash powers.
