Cohen's Immersion Theorem

The immersion set of Cohen is a theorem from the mathematical field of differential topology .

It says that any compact , -dimensional manifold can be immersed in the , where the number of ones is in the dyadic representation of . ${\displaystyle n}$ ${\displaystyle M}$ ${\displaystyle \mathbb {R} ^{2n-a(n)}}$ ${\displaystyle a(n)}$ ${\displaystyle n}$

The theorem improves on Whitney's older immersion theorem , according to which any compact, -dimensional manifold can be immersed into. ${\displaystyle n}$ ${\displaystyle \mathbb {R} ^{2n-1}}$

See also

• Whitney embedding theorem

literature

• Ralph L. Cohen : The Immersion Conjecture for Differentiable Manifolds. Annals of Mathematics, Vol. 122, No. 2, pp. 237-328 (1985).
• Ralph L. Cohen: Immersions of Manifolds. Proc. Nat. Acad. Sci. USA, Vol. 79, pp. 3390–3392, May 1982. ( PDF )