arXiv:1908.10612v6 [math.DG] 8 Jul 2021 Page 1 arXiv:1908.10612v6 [math.DG] 8 Jul 2021
Four Lectures on Scalar Curvature Misha Gromov July 9, 2021 Unlike manifolds with controlled …

We establish several inequalities for manifolds with positive scalar curvature and, more
generally, for the scalar curvature bounded from below. In so far as geometry is concerned …

We use the Dirac operator technique to establish sharp distance estimates for compact spin
manifolds under lower bounds on the scalar curvature in the interior and on the mean …

We prove a homological stability theorem for moduli spaces of manifolds of dimension 2n,
for attaching handles of index at least n, after these manifolds have been stabilised by …

Any smooth manifold can be equipped with a smooth Riemannian metric, that is, a smoothly
varying inner product on each tangent space. A Riemannian metric allows us to do geometry …

We construct infinite rank summands isomorphic to $\mathbb {Z}^\infty $ in the higher
homotopy and homology groups of the diffeomorphism groups of certain $4 $-manifolds …

The study of manifolds and invariants of manifolds was begun more than a century ago. In
this entry we shall discuss the parametrised setting: invariants of families of manifolds …

We present a series of results concerning the interplay between the scalar curvature of a
manifold and the mean curvature of its boundary. In particular, we give a complete …

The Gromov–Lawson–Chernysh surgery theorem | Boletín de la Sociedad Matemática
Mexicana Skip to main content SpringerLink Account Menu Find a journal Publish with us Track …

This is a continuation of our previous work with Botvinnik on the nontriviality of the
secondary index invariant on spaces of metrics of positive scalar curvature, in which we take …