|
7
1
|
This question is a follow-up to my previous question . The statement of the question is the title. Note that the $4$-dimensional real projective space is non-orientable and a characteristic class argument gives that it does not embed in $7$-space. Right now, I am more interested in orientable $4$-manifolds. |
||
|
|
|
14
|
This is true if and only if $X^4$ is spin and its signature vanishes. This is on p. 345 in Gompf/Stipsicz (4-manifolds and Kirby calculus), who cite Ruberman: Imbedding four-manifold and slicing links, 1982. EDIT Of course I mean that $X^4$ CAN be embedded in 6-dimensional space iff the conditions are met. |
|||
|
|
|
6
|
$\mathbb{C}P^2$ does not embed in $\mathbb{R}^6$. See Feder, S.; Segal, D. M. Immersions and embeddings of projective spaces, Proc. Amer. Math. Soc. 35 (1972), 590–592. |
||
|
|
