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/