English

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