The Novikov Conjecture for Linear Groups

By E. Guentner, N. Higson, Shmuel Weinberger. 2005

207 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4929a54934fa8aa804df3cd428442da53196e698

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. Ján Špakula
4. Gilles Pisier
5. E. Guentner
6. Assaf Naor
7. N. Brown
8. Qin Wang

In Mathematical Physics

1. Rufus Willett
2. Guoliang Yu
3. Assaf Naor
4. Ján Špakula
5. Gilles Pisier
6. E. Guentner
7. Romain Tessera
8. Qin Wang

In Statistical and Nonlinear Physics

1. Rufus Willett
2. N. Brown
3. Guoliang Yu
4. E. Guentner
5. Ján Špakula
6. I. Chifan
7. G. Gong
8. Thomas Sinclair

Citations in the corpus

• Finite part of operator K-theory for groups finitely embeddable into Hilbert space and the degree of non-rigidity of manifolds (2013, background): “It is worth noting that the theory of L2 eta invariants developed by Cheeger and Gromov [10] gives some nontrivial information about these kinds of problems; see Geometry & Topology, Volume 19 (2015) Chang and Weinberger [9] and Piazza and Schick [19].”
• Automorphism groups of free groups, surface groups and free abelian groups (2005, background): “bly map between two K-theoretic objects associated to Γ is an isomorphism. Kasparov [51] proved the Novikov conjecture for GL(n,Z), and Guenther, Higson and Weinberger proved it for all linear groups [36]. The BaumConnes conjecture for GL(n,Z) is open when n≥ 4 (cf. [55]). Recently Storm [72] pointe”
• ON THE STRUCTURAL THEORY OF II1 FACTORS OF NEGATIVELY CURVED GROUPS, II. ACTIONS BY PRODUCT GROUPS (2011, background): “(6) all limit groups in the sense of Sela (Λcb(Γ) = 1); this is an observation due to Ozawa based on a result from [19].”
• Property A and the operator norm localization property for discrete metric spaces (2012, background): “We refer to [8] (property A) and [9] (ONL).”
• The Mapping Class Group from the Viewpoint of Measure Equivalence Theory (2005, unknown): “Thus, they are exact by [35].”
• Some notes on Property A (2006, background): “ny groups that have property A, but are not a-T-menable. For example, many linear groups have property T (see section 7.3) so cannot be a-T-menable. They do have property A, however, by the result of [GHW04]. The converse is not known: for example, Thompson’s group F is a-T-menable (this is proved i”
• Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory (2011, result): “Using this result, Guentner, Higson, and Weinberger [11] proved the Novikov conjecture for linear groups.”
• Uniform embeddings of bounded geometry spaces into reflexive Banach space (2003, methodology): “This led to the verification of the Novikov conjecture for large classes of discrete groups, including, for example, linear groups [6] and, more generally, exact groups [12, 7].”
• Tensor Products of C*-Algebras and Operator Spaces (2020, background): “By [99] the same holds when G is any discrete linear group.”
• Simple Lie groups without the approximation property (2012, background): “is factor would then contain a subgroup that is locally isomorphic to either SL(3,R) or Sp(2,R). Let n≥ 1 and let K be field. Then countable discrete subgroups of GL(n,K) are exact. This was proven in [16]. Recall that a lattice in a second countable locally compact group is a closed discrete subgrou”
• Nonlinear spectral calculus and super-expanders (2012, background): “Nevertheless, this weak notion of embedding (much weaker than, say, bi-Lipschitz embeddability) has beautiful applications in geometry and group theory; see [12, 18, 20, 68, 71] and the references therein for examples of such applications.”
• RELATIVE KAZHDAN PROPERTY (2005, background): “2 to the following result, essentially due to [GHW]:”