Composition constructions on diffeomorphisms of S^p × S^q

Reinhard Schultz

Vol. 42 (1972), No. 3, 739–754

DOI: 10.2140/pjm.1972.42.739

Abstract

It is shown that a map from Sp + r to S^p in the image of the J-homomorphism sends particular types of diffeomorphisms of Sp×S^q into diffeomorphisms of S^p+r ×S^q. This is applied to the problem of determining the diffeomorphism type of an exotic (p + q + 7^⋅ + 1)-sphere obtained by attaching D^p+r+1 × lS^q to S^p+r × D^q+1 via a diffeomorphism of Sp + r × Sq.

Mathematical Subject Classification

Primary: 57D50

Milestones

Received: 21 December 1970

Revised: 21 June 1971

Published: 1 September 1972