ON THE HOMOLOGY OF GROUPS OF JETS

[摘要] Let k, n be positive integers. Denote by J(k)+ (n) the Lie group of k-jets at 0 of orientation preserving local diffeomorphisms of R(n) fixing the origin, with multiplication induced by composition of functions. It is a well-known fact that the singular homology of J(k)+ (n) is isomorphic to the singular homology of GL+ (n), the group of n x n matrices with real entries and positive determinant. In this paper we show that the corresponding result is true for the group homology of J(k)+ (n) and GL+ (n) as abstract (discrete) groups. In addition, we show that the continuous (and smooth) cohomology groups of J(k)+ (n) and GL+ (n) are also isomorphic as are the Lie algebra cohomology groups of their Lie algebras.

[发布日期] 1994-03-07