We strengthen a result of Hankeâ€“Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group $C^*$-algebra even holds for the reduced group $C^*$-algebra. To achieve this we provide a Fell absorption principle for certain exotic crossed product functors.

%B arXiv e-prints %P arXiv:1905.07730 %8 May %G eng %0 Journal Article %J ArXiv e-prints %D 2018 %T The Baumâ€“Connes conjecture localised at the unit element of a discrete group %A Paolo Antonini %A Azzali, S. %A Skandalis, G. %K 19K35 %K 46L80 %K 46L85 %K 58J22 %K Mathematics - K-Theory and Homology %K Mathematics - Operator Algebras %B ArXiv e-prints %G eng %0 Journal Article %J ArXiv e-prints %D 2017 %T The injectivity radius of Lie manifolds %A Paolo Antonini %A G. De Philippis %A Nicola Gigli %K (58J40) %K 53C21 %K Mathematics - Differential Geometry %XWe prove in a direct, geometric way that for any compatible Riemannian metric on a Lie manifold the injectivity radius is positive

%B ArXiv e-prints %G eng %U https://arxiv.org/pdf/1707.07595.pdf %0 Journal Article %J ArXiv e-prints %D 2017 %T Integrable lifts for transitive Lie algebroids %A Androulidakis, I. %A Paolo Antonini %K 14F40 %K 58H05 %K Mathematics - Differential Geometry %XInspired by the work of Molino, we show that the integrability obstruction for transitive Lie algebroids can be made to vanish by adding extra dimensions. In particular, we prove that the Weinstein groupoid of a non-integrable transitive and abelian Lie algebroid, is the quotient of a finite dimensional Lie groupoid. Two constructions as such are given: First, explaining the counterexample to integrability given by Almeida and Molino, we see that it can be generalized to the construction of an "Almeida-Molino" integrable lift when the base manifold is simply connected. On the other hand, we notice that the classical de Rham isomorphism provides a universal integrable algebroid. Using it we construct a "de Rham" integrable lift for any given transitive Abelian Lie algebroid.

%B ArXiv e-prints %G eng %U https://arxiv.org/pdf/1707.04855.pdf