Fibred coarse embeddings, a-T-menability and the coarse analogue of the Novikov conjecture

By Martin Finn-Sell. 2013

59 citations recorded by the source corpus.

The connection between the coarse geometry of metric spaces and analytic properties of topological groupoids is well known. One of the main results of Skandalis, Tu and Yu is that a space admits a coarse embedding into Hilbert space if and only if a certain associated topological groupoid is a-T-menable. This groupoid characterisation then reduces the proof that the coarse Baum-Connes conjecture holds for a coarsely embeddable space to known results for a-T-menable groupoids. The property of admitting a fibred coarse embedding into Hilbert space was introduced by Chen, Wang and Yu to provide a property that is sufficient for the maximal analogue to the coarse Baum-Connes conjecture and in this paper we connect this property to the traditional coarse Baum-Connes conjecture using a restriction of the coarse groupoid and homological algebra. Additionally we use this results to give a characterisation of the a-T-menability for residually finite discrete groups.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3f7284b9afbeba685a6a14fc76707afd103bb9b2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Rufus Willett
2. Guoliang Yu
3. Zhizhang Xie

In Mathematical Physics

1. Rufus Willett
2. Guoliang Yu
3. Martin Finn-Sell
4. E. Guentner
5. Ján Špakula
6. Assaf Naor
7. Xiaoman Chen
8. Qin Wang

Citations in the corpus

• Geometric property (T) (2013, result): “The treatment in [18] was quite brief; moreover, we expect that geometric property (T) will see some applications outside of K-theory and higher index theory.”