Let X be quasi-isometric to either the mapping class group equipped with the word metric, or to Teichmüller space equipped with either the Teichmüller metric or the Weil-Petersson metric. We introduce a unified approach to study the coarse geometry of these spaces. We show that the quasi-Lipschitz image in X of a box in R is locally near a standard model of a flat in X . As a consequence, we sh...

The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group Γ, generated by monodromies of the periods ofX . This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase space H(X). We show that, depending on the choice of polarization, the genus g topological string amplitude is either a holomorphic quasi-modular ...

The notion of locally quasi-convex abelian group, introduce by Vilenkin, is extended to maximally almost-periodic non-necessarily abelian groups. For that purpose, we look at certain bornologies that can be defined on the set rep(G) of all finite dimensional continuous representations on a topological group G in order to associate well behaved group topologies (dual topologies) to them. As a co...

For each k = 0, 1, 2, . . . we define an equivalence relation called k-quasi-isotopy on the set of classical links in R3 up to isotopy in the sense of Milnor (1957), such that all sufficiently close approximations of a topological link are k-quasi-isotopic. Whereas 0-quasi-isotopy coincides with link homotopy, 1-quasi-isotopy is not implied by concordance, with aid of the generalized (lk 6= 0) ...

A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such groups are called locally precompact. Within the class of locally precompact groups, the authors classify those groups with the following topological properties: (a) Dieudonné completeness; (b) local realcompactness; (c) r...

The aim of this paper is to study L-fuzzy uniformizable spaces. A new kind of topological fuzzy remote neighborhood system is defined and used for investigating the relationship between L-fuzzy co-topology and L-fuzzy (quasi-)uniformity. It is showed that this fuzzy remote neighborhood system is different from that in [23] when U is an Lfuzzy quasi-uniformity and they will be coincident when U ...