The orbit projection of a proper -manifold is a fibration if and only if all points in are regular. Under additional assumptions we show that is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: is a -quasifibration if and only if all points are regular.
In this paper we show that the multiplicities of holomorphic discrete series representations relative to reductive subgroups satisfy the credo “quantization commutes with reduction”.
Let be a compact lie group. We introduce the set for every smooth manifold . It consists of equivalence classes of pair where is a map which defines a homotopy equivalence from to . Two pairs , for , are equivalent if there is a homotopy equivalence such that is homotopic to .Properties of the set and related to the representation of on the tangent spaces of and at the fixed points. For the case and is the manifold defined by a “linear” action on complex...
In this paper, we calculate the behaviour of the equivariant Quillen metric by submersions. We thus extend a formula of Berthomieu-Bismut to the equivariant case.