In mathematics, a Dold manifold is one of the manifolds P = / τ {\displaystyle P=/\tau }, where τ {\displaystyle \tau } is the involution that acts as −1 on the m-sphere S m {\displaystyle S^{m}} and as complex conjugation on the complex projective space C P n {\displaystyle \mathbb {CP} ^{n}}. Wikipedia