The Coarse Geometric $\ell^p$-Novikov Conjecture for Subspaces of Non-positively Curved Manifolds

TL;DR

This paper proves the coarse geometric $ extit{l}^p$-Novikov Conjecture for metric spaces that can be coarsely embedded into nonpositively curved manifolds, advancing understanding in geometric topology and metric geometry.

Contribution

It establishes the conjecture for a broad class of metric spaces with bounded geometry, linking coarse embeddings and nonpositive curvature.

Findings

Proves the coarse geometric $ extit{l}^p$-Novikov Conjecture for these spaces.

Shows the significance of coarse embeddings into nonpositively curved manifolds.

Extends the scope of the conjecture to new geometric contexts.

Abstract

In this paper, we prove the coarse geometric $\ell^p$-Novikov Conjecture for metric spaces with bounded geometry which admit a coarse embedding into a simply connected complete Riemannian manifold of nonpositive sectional curvature.