The homotopy type of the space of diffeomorphisms. II

Abstract

The result (proved in Part I) that Diff ( D n , ∂ ) ≃ Ω n + 1 ( PL n / O n ) {\operatorname {Diff}}({D^n},\partial ) \simeq {\Omega ^{n + 1}}({\text {PL}_n}/{O_n}) is used to compute some new homotopy of Diff ( D n , ∂ D n ) {\operatorname {Diff}}({D^n},\partial {D^n}) . The relation between smooth and PL pseudo-isotopy is explored. Known and new results on the homotopy of PL n {\text {PL}_n} are summarized.