✦ LIBER ✦

Lipschitz–Killing Invariants

✍ Scribed by Andreas Bernig; Ludwig Bröcker

Book ID: 101379437
Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 273 KB
Volume: 245
Category: Article
ISSN: 0025-584X
DOI: 10.1002/1522-2616(200211)245:1<5::aid-mana5>3.0.co;2-e

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✦ Synopsis

We define and characterize Lipschitz-Killing invariants for lattices of compact sufficiently tame subsets of IR N .

Our main example are definable subsets with respect to an o-minimal system ω. We also investigate the ring M 0 (ω), which is the metric counterpart of the universal ring K 0 (ω). The Lipschitz-Killing invariants give rise to a homomorphism M 0 (ω) → IR[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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