In mathematics, a Dold manifold is one of the manifolds

P(m,n) = (S^m \times \mathbb^n)/\tau

, where

\tau

is the involution that acts as −1 on the ''m''-sphere

S^m

and as

complex conjugation In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, if a and b are real numbers, then the complex conjugate of a + bi is a - ...

on the

complex projective space In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space label the lines through the origin of a real Euclidean space, the points of a ...

\mathbb^n

. These manifolds were constructed by , who used them to give explicit generators for

René Thom René Frédéric Thom (; 2 September 1923 – 25 October 2002) was a French mathematician, who received the Fields Medal in 1958. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became ...

's unoriented cobordism ring. Note that

P(m,0)=\mathbb^m

, the

real projective space In mathematics, real projective space, denoted or is the topological space of lines passing through the origin 0 in the real space It is a compact, smooth manifold of dimension , and is a special case of a Grassmannian space. Basic properti ...

of dimension ''m'', and

P(0,n)=\mathbb^n

References

{{Reflist Algebraic topology Manifolds