In mathematics, a Dold manifold is one of the manifolds , where is the involution that acts as −1 on the m-sphere and as complex conjugation on the complex projective space . 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 , the real projective space of dimension m, and .[3]

References

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  1. ^ Dold, Albrecht (1956), "Erzeugende der Thomschen Algebra  ", Mathematische Zeitschrift, 65 (1): 25–35, doi:10.1007/BF01473868, ISSN 0025-5874, MR 0079269
  2. ^ "Dold manifold". www.map.mpim-bonn.mpg.de. The Manifold Atlas Project. Retrieved May 2, 2022.
  3. ^ 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.