Topologically, quasiconformally or Lipschitz locally flat approximation of embeddings

Amenability, Locally Finite Spaces, and Bi-lipschitz Embeddings

We define the isoperimetric constant for any locally finite metric space and we study the property of having isoperimetric constant equal to zero. This property, called Small Neighborhood property, clearly extends amenability to any locally finite space. Therefore, we start making a comparison between this property and other notions of amenability for locally finite metric spaces that have been...

TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

Metric Embeddings and Lipschitz Extensions

Quantitative Bi-Lipschitz embeddings of manifolds

The goal of this write up is to provide a more detailed proof of the collapsing result already contained in [2]. While reading this paper the author struggled to understand many details of the proofs, particularly where the details of an argument were spread over several papers or simply assumed obvious. Nothing new is proven in this write up, but results are explicated and an attempt is made t...

Superfluidity in topologically nontrivial flat bands.

Topological invariants built from the periodic Bloch functions characterize new phases of matter, such as topological insulators and topological superconductors. The most important topological invariant is the Chern number that explains the quantized conductance of the quantum Hall effect. Here we provide a general result for the superfluid weight Ds of a multiband superconductor that is applic...