A note on local change of diffeomorphism

Masuda, Mikiya

doi:10.1090/S0002-9947-1989-0979960-6

A note on local change of diffeomorphism
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by Mikiya Masuda PDF

Trans. Amer. Math. Soc. 316 (1989), 555-566 Request permission

Abstract:

Let $D(M)$ be the group of pseudo-isotopy classes of orientation preserving diffeomorphisms of a compact manifold $M$ which restrict to the identity on $\partial M$. If a compact manifold $N$ of the same dimension as $M$ is embedded in $M$, then extending maps in $D(N)$ as the identity on the exterior of $N$ defines a homomorphism $E:D(N) \to D(M)$. We ask if the kernel of $E$ is finite and show that this is the case for special cases.

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