Amenable group actions and the Novikov conjecture

By N. Higson, J. Roe. 2000

248 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/28ed51e7d024cd3f804811ae8b44aed0c96500c2

How researchers see this paper

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

In Geometry and Topology

1. Rufus Willett
2. E. Guentner
3. Guoliang Yu
4. Nathanial P. Brown Narutaka Ozawa
5. Y. Kida
6. Gregory C. Bell
7. K. Fujiwara
8. Martin Finn-Sell

In Mathematical Physics

1. Rufus Willett
2. Guoliang Yu
3. E. Guentner
4. Nathanial P. Brown Narutaka Ozawa
5. Martin Finn-Sell
6. Ján Špakula
7. Gregory C. Bell
8. Y. Kida

Citations in the corpus

• Bivariant K-theory and the Novikov conjecture (2000, methodology): “We aim to prove the following result, which is an extension of Theorem 1.2 in [ HR2 ].”
• Fibred coarse embeddings, a-T-menability and the coarse analogue of the Novikov conjecture (2013, background): “sembly map µ∗ is an isomorphism. Many metric spaces admit coarse embeddings; the property is a suitably flexible one as it is implied by many other coarse properties such as finite asymptotic dimension [HR00], or the weaker properties of finite decomposition complexity [GTY12] and property A [Yu00]. Th”
• Boundary amenability of relatively hyperbolic groups (2005, methodology): “(See [ AR ][Ka] for simpler proofs.) In this paper, we study the case of relatively hyperbolic groups.”
• The coarse Baum–Connes conjecture for spaces which admit a uniform embedding into Hilbert space (2000, background): “It follows that discrete subgroups of connected Lie groups have property A [17].”
• Geometry of the mapping class groups I: Boundary amenability (2005, background): “By an observation of Higson and Roe [ 17 ], this is equivalent to boundary amenability for the mapping class groups.”
• Squeezing and Higher Algebraic K-Theory (2003, background): “Groups of finite asymptotic dimension admit such a uniform embedding by [HR00].”
• Coarse Non-Amenability and Coarse Embeddings (2011, background): “For a countable discrete group Γ, it is equivalent to the existence of a topological amenable action of Γ on a compact Hausdorff space and to the C∗-exactness of the reduced C∗-algebra C∗ r (Γ) [12, 8].”
• ON THE STRUCTURAL THEORY OF II1 FACTORS OF NEGATIVELY CURVED GROUPS, II. ACTIONS BY PRODUCT GROUPS (2011, background): “[11]) Let Γ be a countable discrete group and Γ X be an action of Γ by homeomorphisms on a compact topological space X.”
• Amenable actions and exactness for discrete groups (2000, methodology): “2 in [HR] and there is a delicate problem when we are dealing with non second countable space, but this is justified when G is countable.”