Etude topologique de lʹespace des homéomorphismes de Brouwer, II

In this paper, sequel to Le Roux (Etude topologique de l ʹespace des homéomorphismes de Brouwer, I), we persue the study of the space B of the fixed point free orientation preserving homeomorphisms of the plane, and of the subspace Bτ consisting of the homeomorphisms that are conjugate to an affine translation. We first give another derivation of the weak homotopy type of the pair (B, Bτ); and then show that the space Bτ is an absolute neighbourhood retract (ANR), homeomorphic to the product of the circle and the separable Hilbert space.