A topological spectrum is an object of stable homotopy theory represented, in a sequential model, by based spaces 
and structure maps 
. Here 
denotes reduced suspension, obtained by smashing with
the based circle. Its stable homotopy groups
are
 |
Stable equivalences identify maps inducing isomorphisms on these groups. A finite spectrum is one obtained from finitely many sphere cells, up to stable equivalence. Spectra represent generalized homology and cohomology theories, and their smash product gives the stable homotopy category its tensor structure. The sphere spectrum is its unit.
