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Bilipschitz invariance of the first transverse characteristic map

Michel Hilsum (2012)

Banach Center Publications

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.

Bipartite knots

Sergei Duzhin, Mikhail Shkolnikov (2014)

Fundamenta Mathematicae

We give a solution to a part of Problem 1.60 in Kirby's list of open problems in topology, thus answering in the positive the question raised in 1987 by J. Przytycki.

Boundaries of right-angled hyperbolic buildings

Jan Dymara, Damian Osajda (2007)

Fundamenta Mathematicae

We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. As a consequence, the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.

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