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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.

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.

Citations

17 citations in Web of Science®
13 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Integral geometry;o–minimal geometry;normal cycles
Language:English
Date:November 2002
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:25
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0025-584X
Publisher DOI:10.1002/1522-2616(200211)245:1<5::AID-MANA5>3.0.CO;2-E
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1936341
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1074.53064

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