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163 views

Uniqueness of collar neighborhoods for non-compact boundary case in smooth setting

Let $M$ be a smooth manifold and let $f_0, f_1 \colon [0, 1] \times \partial M \to M$ be two smooth embeddings that are the identity map on $\partial M \times\{0\} = \partial M$ . If $\partial M$ is …
1 vote
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129 views

Codimension one submanifold gives cofibrant pair

Let $M$ be a smooth manifold, and $N$ be an embedded smooth submanifold of $M$ with $\partial M=\varnothing=\partial N$. Suppose, $\dim M-\dim N=1$, and $N$ is a closed subset of $M$. Does the inclus …