Given a smooth S¹-foliated bundle, A. Connes has shown the existence of an additive morphism ϕ 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 C¹ by H. Natsume.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-10,
author = {Michel Hilsum},
title = {Bilipschitz invariance of the first transverse characteristic map},
journal = {Banach Center Publications},
volume = {97},
year = {2012},
pages = {245-260},
zbl = {1269.46054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-10}
}
Michel Hilsum. Bilipschitz invariance of the first transverse characteristic map. Banach Center Publications, Tome 97 (2012) pp. 245-260. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-10/