Dold manifold

In mathematics, a Dold manifold is one of the manifolds [math]\displaystyle{ P(m,n) = (S^m \times \mathbb{CP}^n)/\tau }[/math], where [math]\displaystyle{ \tau }[/math] is the involution that acts as −1 on the m-sphere [math]\displaystyle{ S^m }[/math] and as complex conjugation on the complex projective space [math]\displaystyle{ \mathbb{CP}^n }[/math]. These manifolds were constructed by Albrecht Dold (1956), who used them to give explicit generators for René Thom's unoriented cobordism ring. Note that [math]\displaystyle{ P(m,0)=\mathbb{RP}^m }[/math], the real projective space of dimension m, and [math]\displaystyle{ P(0,n)=\mathbb{CP}^n }[/math].

References

• Dold, Albrecht (1956), "Erzeugende der Thomschen Algebra [math]\displaystyle{ \mathcal{N} }[/math]", Mathematische Zeitschrift 65 (1): 25–35, doi:10.1007/BF01473868, ISSN 0025-5874