Gromov positive scalar curvature conjecture and rationally inessential macroscopically large manifolds
Geometric Topology
2016-03-01 v3 Algebraic Topology
Differential Geometry
Group Theory
Abstract
We give the first examples of rationally inessential but macroscopically large manifolds. Our manifolds are counterexamples to the Dranishnikov rationality conjecture. For some of them we prove that they do not admit a metric of positive scalar curvature, thus satisfy the Gromov positive scalar curvature conjecture. Fundamental groups of our manifolds are finite index subgroups of right angled Coxeter groups. The construction uses small covers of convex polyhedrons (or alternatively Davis complexes) and surgery.
Keywords
Cite
@article{arxiv.1408.0372,
title = {Gromov positive scalar curvature conjecture and rationally inessential macroscopically large manifolds},
author = {Michał Marcinkowski},
journal= {arXiv preprint arXiv:1408.0372},
year = {2016}
}
Comments
13 pages; a new proof of Lemma 7; there was a mistake in 4.1, the whole subsection was removed