Diffeomorphisms almost regularly homotopic to the identity
Abstract: Let be a self-map of a closed smooth n-manifold. Does there exist a diffeomorphism homotopic to f? Define to be almost regularly homotopic to the identity if . is regularly homotopic to the inclusion . Let be the result of collapsing the boundary of a smooth n-cell in M, and let be the codiagonal. For define to be the composition
Theorem. If M is 2-connected, s-parallelizable, and with , then contains a diffeomorphism almost regularly homotopic to the identity iff is in the kernel of the stabilization map .
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Keywords: Diffeomorphism, Postnikov tower, cobordism, stable homotopy, mapping torus
Article copyright: © Copyright 1978 American Mathematical Society