Bilipschitz invariance of the first transverse characteristic map
Volume 98 / 2012
Banach Center Publications 98 (2012), 245-260
MSC: Primary 46L, 53C; Secondary 48L80, 46L87, 53C12, 57R32.
DOI: 10.4064/bc98-0-10
Abstract
Given a smooth $S^1$-foliated bundle, A. Connes has shown the existence of an additive morphism $\phi$ from the K-theory group of the foliation C*-algebra to the scalar field, which factorizes, via the assembly map, the Godbillon-Vey class, which is the first secondary characteristic class, of the classifying space. We prove the invariance of this map under a bilipschitz homeomorphism, extending a previous result for maps of class $C^1$ by H. Natsume.
