A class of infinite dimensional subgroups of Diff^r (X) which are Banach Lie groups

Wendell Dan Curtis, Yu-Lee Lee and Forrest Miller

Vol. 47 (1973), No. 1, 59–65

DOI: 10.2140/pjm.1973.47.59

Abstract

It is known that if X is a compact C^∞-manifold then Diff ^r(X) with the usual manifold structure is a Banach manifold but not a Banach Lie group. In this paper we construct a class of infinite dimensional subgroups of Diff ^r(X) which are Banach Lie groups.

Mathematical Subject Classification 2000

Primary: 58D05

Secondary: 22E65

Milestones

Received: 7 March 1972

Published: 1 July 1973