On Gromov's scalar curvature conjecture

2009/01/28 by Bolotov, Dmitry, Dranishnikov, Alexander · 1 citation
#53C23 #55M30 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.0901.4503

Abstract

We prove the Gromov conjecture on the macroscopic dimension of the universal covering of a closed spin manifold with a positive scalar curvature under the following assumptions on the fundamental group: 1. The Strong Novikov Conjecture holds for π. 2. The natural map per:ko_n(Bπ)→ KO_n(Bπ) is injective.

Cited by

• Minimal surfaces and comparison geometry

Related

• On Gromov's positive scalar curvature conjecture for virtual duality\n groups
• On Gromov's conjecture for totally non-spin manifolds
• On Gromov's conjecture for right-angled Artin groups
• The Gromov-Lawson-Rosenberg conjecture for some finite groups
• On macroscopic dimension of universal coverings of closed manifolds