Collar area

In the mathematical field of differential topology , a neighborhood of the edge of a differentiable manifold is called a collar neighborhood if it is diffeomorphic to the product . ${\ displaystyle \ partial M}$ ${\ displaystyle M}$ ${\ displaystyle \ partial M \ times \ left [0,1 \ right]}$

A Milnor theorem ( Milnor's collar neighborhood theorem ) guarantees the existence of a collar neighborhood of the boundary for every differentiable manifold with a boundary. This theorem follows from the theorem of the tubular neighborhood and the triviality of the normal bundle of . ${\ displaystyle \ partial M}$ ${\ displaystyle \ partial M \ subset M}$

The corollary shows that inclusion is a homotopy equivalence . ${\ displaystyle (M- \ partial M) \ hookrightarrow M}$

Individual evidence

^ Corollary 3.5 in: John Milnor , Lectures on the h-cobordism theorem. Notes by L. Siebenmann and J. Sondow Princeton University Press, Princeton, NJ 1965, online (pdf)

[1] Corollary 3.5 in: John Milnor , Lectures on the h-cobordism theorem. Notes by L. Siebenmann and J. Sondow Princeton University Press, Princeton, NJ 1965, online (pdf)