Topological study of the space of Brouwer homeomorphisms, part II

In this paper, sequel to Le Roux (Etude topologique de l'espace des homeomo rphismes de Brouwer, I), we persue the study of the space B of the fixed po int free orientation preserving homeomorphisms of the plane, and of the sub space B-t 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, B-t); and then show that the space B-t is an absolute neighbou rhood retract (ANR), homeomorphic to the product of the circle and the sepa rable Hilbert space. (C) 2001 Elsevier Science Ltd. All rights reserved.