The coarse geometric Novikov conjecture and uniform convexity
  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. 
Gennadi Kasparov and Guoliang Yu