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In differential topology, the Whitney immersion theorem (named after Hassler Whitney) states that for m > 1 {\displaystyle m>1} , any smooth m {\displaystyle...

2n − 1. This last result is sometimes called the Whitney immersion theorem. The weak Whitney embedding is proved through a projection argument. When the...

homotopic to an immersion, and in fact to an embedding for 2m < n; these are the Whitney immersion theorem and Whitney embedding theorem. Stephen Smale...

work in manifolds, embeddings, immersions, characteristic classes, and geometric integration theory. Hassler Whitney was born on March 23, 1907, in New...

Whitehead theorem (homotopy theory) Whitney embedding theorem (differential manifolds) Whitney extension theorem (mathematical analysis) Whitney immersion theorem...

as immersions, submersions, covering spaces, and ramified covering spaces. Basic results include the Whitney embedding theorem and Whitney immersion theorem...

to homotopy, particularly for immersions. The first evidence of h-principle appeared in the Whitney–Graustein theorem. This was followed by the Nash–Kuiper...

as immersions, submersions, covering spaces, and ramified covering spaces. Basic results include the Whitney embedding theorem and Whitney immersion theorem...

unrestricted choice of f in the Nash–Kuiper theorem. For example, the image of any smooth isometric hypersurface immersion of the round sphere must itself be a...

embeddings and immersions include: Whitney embedding theorem Whitney immersion theorem Nash embedding theorem Smale-Hirsch theorem Key tools in studying these...

homeomorphisms, and smooth immersions are all locally injective functions that are not necessarily injective. The inverse function theorem gives a sufficient...

not by isotopy. The Whitney–Graustein theorem classifies the regular homotopy classes of a circle into the plane; two immersions are regularly homotopic...

is equivalent to the usual, abstract approach, because, by the Whitney embedding theorem, any second-countable smooth (abstract) m {\displaystyle m} -manifold...

because the Whitney embedding theorem, the key technical trick which underlies surgery theory, requires 2+1 dimensions. Roughly, the Whitney trick allows...

submersion immersion Embedding Whitney embedding theorem Critical value Sard's theorem Saddle point Morse theory Lie derivative Hairy ball theorem Poincaré–Hopf...

fixed-point theorem Chern's conjecture (affine geometry) Differential structure Homotopy principle Immersion (mathematics) Whitney embedding theorem Morris...

geometry. This work, also introducing a preliminary form of the Nash–Moser theorem, was later recognized by the American Mathematical Society with the Leroy...

\mathbb {R} ^{n+1}} admits eversion. Nylon string open model Whitney–Graustein theorem Bednorz, Adam; Bednorz, Witold (2019). "Analytic sphere eversion...

makes use of a partition of unity. An alternative proof uses the Whitney embedding theorem to embed M {\displaystyle M} into Euclidean space and then pulls...

Famous theorems in differential topology include the Whitney embedding theorem, the hairy ball theorem, the Hopf theorem, the Poincaré–Hopf theorem, Donaldson's...