/sci/ - Science & Math

>>14998859
If we're being literal about it every manifold embeds in [math]\mathbb{R}^n[/math], so they're all restrictions of [math]\mathbb{R}^n[/math]

Practically speaking, there are also topological techniques for manifold construction like surgery, and also spin groups, moduli spaces and random non-generic constructions like spaces of basis for some vector space, and a bunch of other ways that I either don't know about or am not remembering right now.
Algebraic geometry also has blow-ups and probably other stuff, but I'm not sure how often the results of that are manifolds.