The product on smooth and generalized valuations (Q2881361)

The author investigates the product of smooth and generalized valuations. On a smooth manifold \(X\), one considers the system \(P\) of all compact submanifolds with corners and calls a finitely additive functional on \(P\) a valuation on \(X\). The reviewer cannot do better than the authors' summary: ``The product of smooth valuations on manifolds is described in terms of differential forms, Gelfand transforms, and blow-up spaces. It is known that the product extends partially to generalized valuations and corresponds geometrically to transversal intersections. This result is used to prove a general kinematic formula on compact rank one symmetric spaces.''