The space of immersions of a manifold in another manifold is homotopically equivalent to the space of bundle injections from the tangent space of the first to the tangent bundle of the second.
Smale-Hirsch Theorem
See also
Homotopy, Immersion, Manifold, Tangent Bundle, Tangent SpaceExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Smale-Hirsch Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Smale-HirschTheorem.html