# Lipschitz-Killing invariants

Bernig, A; Bröcker, L (2002). Lipschitz-Killing invariants. Mathematische Nachrichten, 245:5-25.

## Abstract

We define and characterize Lipschitz–Killing invariants for lattices of compact sufficiently tame subsets of ℝN. Our main example are definable subsets with respect to an o–minimal system ω. We also investigate the ring M0(ω), which is the metric counterpart of the universal ring K0(ω). The Lipschitz–Killing invariants give rise to a homomorphism M0(ω) ↦ ℝ[t], the kernel of which is the closure of {0}. Here the construction of suitable topologies plays an essential role. The results are also interpreted in terms of spherical currents.

## Abstract

We define and characterize Lipschitz–Killing invariants for lattices of compact sufficiently tame subsets of ℝN. Our main example are definable subsets with respect to an o–minimal system ω. We also investigate the ring M0(ω), which is the metric counterpart of the universal ring K0(ω). The Lipschitz–Killing invariants give rise to a homomorphism M0(ω) ↦ ℝ[t], the kernel of which is the closure of {0}. Here the construction of suitable topologies plays an essential role. The results are also interpreted in terms of spherical currents.

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