• Source: Dold manifold

In mathematics, a Dold manifold is one of the manifolds



P
(
m
,
n
)
=
(

S

m


×


C
P


n


)

/

τ


{\displaystyle P(m,n)=(S^{m}\times \mathbb {CP} ^{n})/\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}}

. These manifolds were constructed by Albrecht Dold (1956), who used them to give explicit generators for René Thom's unoriented cobordism ring. Note that



P
(
m
,
0
)
=


R
P


m




{\displaystyle P(m,0)=\mathbb {RP} ^{m}}

, the real projective space of dimension m, and



P
(
0
,
n
)
=


C
P


n




{\displaystyle P(0,n)=\mathbb {CP} ^{n}}

.




References

Kata Kunci Pencarian:

• Dold manifold
• Albrecht Dold
• List of cohomology theories
• Algebraic topology
• Cohomology
• Herbert Seifert
• Almgren's isomorphism theorem
• Lefschetz fixed-point theorem
• Simplicial group
• Almgren–Pitts min-max theory