Let S be a flat surface, such as the Euclidean plane. We obtain direct characterizations of the connected components of the space of all curves on S which start and end at given points in given directions, and whose curvatures are constrained to lie in a given interval, in terms of all parameters involved. Many topological properties of these spaces are investigated. Some conjectures of L. E. D...

Definition(s): Let G = (V,E) be a graph. A set S ⊆ V is called separating in G if G− S is not connected. The connectivity of G, written κ(G), is the minimum size of a set S, such that G−S is not connected or has only one vertex. A separating set in G with cardinality κ(G) is called a κ-set in G. Let G1 = (V1, E1) and G2 = (V2, E2) be a graphs. Strong product G1 G2 of graphs G1 and G2 is the gra...

Following up on our earlier work and the work of N. Karpenko and A. Merkurjev, we study the essential p-dimension of linear algebraic groups G whose connected component G is a torus.

Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C *-algebra of G is an isomorphism.

Article history: Received 1 October 2012 Received in revised form 9 February 2015 Accepted 10 February 2015 Available online 14 February 2015

Let ∆ ⊆ C be the open unit disc and let Σ ⊆ ∆×∆ be a compact set such that K = Σ ∪ (∂∆×∆) is a connected set. It is a classical result by Hartogs that if Σ is an analytic variety over ∆ with the boundary in ∂∆×∆, then every function holomorphic in a connected neighbourhood of K extends holomorphically to a neighbourhood of ∆ × ∆. It is proved that the same conclusion holds if Σ is a ‘continuous...

In this paper we give the asymptotic growth of the number of connected components of the moduli space of surfaces of general type corresponding to certain families of Beauville surfaces with group either PSL(2, p), or an alternating group, or a symmetric group or an abelian group. We moreover extend these results to regular surfaces isogenous to a higher product of curves.

We give a general exposition of model theoretic connected components of groups. We show that if a group G has NIP, then there exists the smallest invariant (over some small set) subgroup of G with bounded index (Theorem 5.4). This result extends theorem of Shelah from [14]. We consider also in this context the multiplicative and the additive groups of an infinite field.

We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the subcomponents corresponding to a minimum partition. This minimum partition Pmin is induced by the deletion of the minimum weight edges. We provide a characterization of the graphs satisfying inherita...

Let S be a complete flat surface, such as the Euclidean plane. We determine the homeomorphism class of the space of all curves on S which start and end at given points in given directions and whose curvatures are constrained to lie in a given open interval, in terms of all parameters involved. Any connected component of such a space is either contractible or homotopy equivalent to an n-sphere, ...