Dold manifold

In mathematics, a Dold manifold is one of the manifolds $P(m,n)=(S^m\times {ℂ\mathbb{P}}^n)/\tau$, where $\tau$ is the involution that acts as −1 on the m-sphere $S^m$ and as complex conjugation on the complex projective space ${ℂ\mathbb{P}}^n$. These manifolds were constructed by Template:Harvs, who used them to give explicit generators for René Thom's unoriented cobordism ring. Note that $P(m,0)={ℝ\mathbb{P}}^m$, the real projective space of dimension m, and $P(0,n)={ℂ\mathbb{P}}^n$.