Dold manifold

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