1,408 research outputs found
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.Comment: 64 pages, to appear in Advances in Mathematic
The Novikov conjecture on Cheeger spaces
We prove the Novikov conjecture on oriented Cheeger spaces whose fundamental
group satisfies the strong Novikov conjecture. A Cheeger space is a stratified
pseudomanifold admitting, through a choice of ideal boundary conditions, an
L2-de Rham cohomology theory satisfying Poincare duality. We prove that this
cohomology theory is invariant under stratified homotopy equivalences and that
its signature is invariant under Cheeger space cobordism. Analogous results,
after coupling with a Mishchenko bundle associated to any Galois covering,
allow us to carry out the analytic approach to the Novikov conjecture: we
define higher analytic signatures of a Cheeger space and prove that they are
stratified homotopy invariants whenever the assembly map is rationally
injective. Finally we show that the analytic signature of a Cheeger space
coincides with its topological signature as defined by Banagl.Comment: To appear in JNC
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