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Kinematic and tube formulas for piecewise linear spaces. (English) Zbl 0615.53058
The Lipschitz-Killing curvatures of a piecewise linear (p.l.) space are close to those of a smooth space if the p.l. space approximates the smooth space suitably. These curvatures appear in various contexts, such as in the asymptotics of the heat kernel on a p.l. space, and in attempts to quantize gravity using the Regge calculus. This article shows how the Lipschitz-Killing curvatures of p.l. spaces appear in versions of Chern’s kinematic formula and Weyl’s tube formula for p.l. spaces.
Reviewer: J.Hebda

53C65 Integral geometry
57Q99 PL-topology
53A17 Differential geometric aspects in kinematics
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