Integral Künneth torsion polynomial (source code)

= Integral Künneth torsion polynomial
{title2=$T_{A\times B}=F_AT_B+T_AF_B+(1+t^{-1})T_AT_B$}

For spaces whose integral <cohomology> has only free and $\mathbb Z/2$ summands, let $F$ encode free ranks and $T$ count order-two summands by degree. An additively split integral <Künneth theorem> gives $F_{A\times B}=F_AF_B$ and the displayed rule for $T$. The $t^{-1}$ term is the cohomological degree shift of the <Tor functor> contribution. The formula requires this torsion type and the usual finite-type hypotheses.