Surgery and handle straightening in Hilbert cube manifolds

Thomas Ashland Chapman

Vol. 45 (1973), No. 1, 59–79

DOI: 10.2140/pjm.1973.45.59

Abstract

The main result of this paper establishes an infinite dimensional version of the finite-dimensional handle straightening result of Kirby-Siebenmann. In order to do this a procedure is developed for doing surgery on infinite-dimensional manifolds. These results are used elsewhere to prove that every compact Hilbert cube manifold can be triangulated and to establish the topological invariance of Whitehead torsion.

Mathematical Subject Classification

Primary: 57A20

Milestones

Received: 12 June 1972

Published: 1 March 1973