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 −1 on the m-sphere $S^{m}$ and as complex conjugation on the complex projective space $\mathbb {CP} ^{n}$ . These manifolds were constructed by Albrecht Dold (1956),^[1] who used them to give explicit generators for René Thom's unoriented cobordism ring.^[2] Note that $P(m,0)=\mathbb {RP} ^{m}$ , the real projective space of dimension m, and $P(0,n)=\mathbb {CP} ^{n}$ .^[3]

References

^ Dold, Albrecht (1956), "Erzeugende der Thomschen Algebra ${\mathcal {N}}$ ", Mathematische Zeitschrift, 65 (1): 25–35, doi:10.1007/BF01473868, ISSN 0025-5874, MR 0079269
^ "Dold manifold". www.map.mpim-bonn.mpg.de. The Manifold Atlas Project. Retrieved May 2, 2022.
^ Ucci, John James (1965). "Immersions and embeddings of Dold manifolds" (PDF). Topology. 4 (3): 283–293. doi:10.1016/0040-9383(65)90012-1. MR 0187250.