AN ISOTOPY EXTENSION ON OPEN MANIFOLDS

Abstract

Let $M$ be a compact topological manifold of $\operatorname{dim} \geq 5$, with connected boundary $\partial M$. Let $T O P(M)$ be the simplicial group of homeomorphisms and denote the interior of $M$ by Int $M$. Let $f: \operatorname{TOP}(M) \rightarrow \operatorname{TOP}($ Int $M)$ be the restriction map and let $\mathcal{G}$ be the homotopy fiber of $f$ over the $\operatorname{id}_{\operatorname{Int} M}$. We proved that $\pi_0 \mathcal{G}$ is isomorphic to $\pi_0 \mathcal{C}(\partial M)$, where $\mathcal{C}(\partial M)$ is the concordance space of $\partial M$.

Received: October 8, 2024
Accepted: November 12, 2024