The coarse geometric Novikov conjecture and uniform convexity

By G. Kasparov, Guoliang Yu. 2005

134 citations recorded by the source corpus.

Abstract The coarse geometric Novikov conjecture provides an algorithm to determine when the higher index of an elliptic operator on a noncompact space is nonzero. The purpose of this paper is to prove the coarse geometric Novikov conjecture for spaces which admit a (coarse) uniform embedding into a uniformly convex Banach space.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1c174c2001ad085672dee723ef0771166439928f

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

COARSE AND UNIFORM EMBEDDINGS INTO REFLEXIVE SPACES (2007, result): “This results from the work of Yu [28] and Kasparov and Yu [18] who show that such metric spaces with bounded geometry which coarsely embed into a uniformly convex space satisfy the coarse Novikov conjecture.”
Nonlinear spectral calculus and super-expanders (2012, methodology): “It is also unknown whether there exist graph families of bounded degree and logarithmic girth that do not admit a coarse embedding into any super-reflexive normed space; this question is of particular interest in the context of the potential application to the Novikov conjecture that was proposed by”
The non-linear geometry of Banach spaces after Nigel Kalton (2012, unknown): “This important result was later generalized by Kasparov and Yu [61] who showed that the Hilbert space can be replaced in this statement by any super-reflexive space.”
Geometrization of the Strong Novikov Conjecture for residually finite groups (2008, background): “More generally, Kasparov and Yu proved the Coarse Geometric Novikov Conjecture for bounded geometry metric spaces which are coarsely embeddable into uniformly convex Banach spaces [16].”
l~p (p > 2) does not coarsely embed into a Hilbert space (2004, methodology): “into a Hilbert space, and in [ KY ] G. Kasparov and Yu proved that to get the same conclusion it is sufficient that the metric space coarsely embeds into a uniformly convex Banach space.”
Complex Interpolation between Hilbert, Banach and Operator spaces (2008, background): “In connection with the Baum–Connes conjecture (see [24, 70, 37]) it is of interest to understand in which Banach spaces X we can embed coarsely, but uniformly over m, such a sequence {G(m)} viewed as a sequence of metric spaces.”
The asymptotic dimension of a curve graph is finite (2005, result): “This result has since been improved upon by Yu [40] and Kasparov-Yu [26].”
Comparison of Metric Spectral Gaps (2013, methodology): “of super-expanders (see [75]) with logarithmic girth, a result which could then be used in conjunction with Gromov’s random group construction [39] to rule out the success of an approach to the Novikov conjecture that was discovered by Kasparov and Yu [49].”