= Mod-two cohomology ring of an inversion mapping torus
{title2=$H^*(M_n;\mathbb F_2)=\mathbb F_2[t,x_1,\ldots,x_{n-1}]/(t^2,x_i^2+tx_i)$}
The base class $t$ and coordinate classes $x_i$ all have degree one. Pullback of the <mod-two intersection pairing of the Klein bottle> gives $x_i^2=t x_i$. The <Leray-Hirsch theorem> gives the basis consisting of square-free products $x_I$ and $t x_I$. Thus the additive dimensions match those of a <torus>, but the degree-one squares differ for $n\geq2$.
Back to article page
