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The product on smooth and generalized valuations
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 134, Number 2, April 2012
- pp. 507-560
- 10.1353/ajm.2012.0011
- Article
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The product of smooth valuations on manifolds is described in terms of differential forms,
Gelfand transforms, and blow-up spaces. It is shown 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.