Differentiable approximations to homotopy resolutions and framed cobordism

Donald William Kahn

Vol. 113 (1984), No. 2, 373–382

DOI: 10.2140/pjm.1984.113.373

Abstract

The determination of homotopy groups of spheres remains a central problem in algebraic topology. The various methods for addressing this problem cover some considerable ground, from intricate algebra to the structure of manifolds. Our general purpose here is to show that the gap between some of these methods can in fact be closed, and that one may find geometric structures (manifolds) which reflect the filtrations arising from algebraic methods.

Mathematical Subject Classification 2000

Primary: 57R90

Secondary: 55Q40

Milestones

Received: 20 September 1982

Revised: 16 March 1983

Published: 1 August 1984