C0 coarse geometry and scalar curvature

Asymptotic upper curvature bounds in coarse geometry

We define a notion of an asymptotic upper curvature bound for Gromov hyperbolic metric spaces that is invariant under rough-isometries and examine the basic properties of this concept.

C0-coarse Geometry of Complements of Z-sets in the Hilbert Cube

Motivated by the Chapman Complement Theorem, we construct an isomorphism between the topological category of compact Z-sets in the Hilbert cube Q and the C0-coarse category of their complements. The C0coarse morphisms are, in this particular case, intrinsically related to uniformly continuous proper maps. Using that fact we are able to relate in a natural way some of the topological invariants ...

Coarse Geometry and Randomness

1 Introductory graph and metric notions 5 1.1 The Cheeger constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Expander graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Isoperimetric dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.5 Rough isome...

Positive Scalar Curvature and Surgery

Positive Scalar Curvature

One of the striking initial applications of the Seiberg-Witten invariants was to give new obstructions to the existence of Riemannian metrics of positive scalar curvature on 4– manifolds. The vanishing of the Seiberg–Witten invariants of a manifold admitting such a metric may be viewed as a non-linear generalization of the classic conditions [12, 11] derived from the Dirac operator. If a manifo...