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Lipschitz–Killing Invariants
Author(s) -
Bernig Andreas,
Bröcker Ludwig
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200211)245:1<5::aid-mana5>3.0.co;2-e
Subject(s) - mathematics , lipschitz continuity , homomorphism , pure mathematics , ring (chemistry) , closure (psychology) , kernel (algebra) , metric (unit) , topology (electrical circuits) , combinatorics , chemistry , operations management , organic chemistry , economics , market economy
We define and characterize Lipschitz–Killing invariants for lattices of compact sufficiently tame subsets of ℝ 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 ) ↦ 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.