∇ : V → V ⊗ ΩX . Then the flat sections of V determine a local system L on X. For every point x ∈ X, the fiber of the local system Lx can be identified with the fiber Vx. Given a path p : [0, 1] from x = p(0) to y = p(1), there is a map p! : Lx → Ly is given by parallel transport along p, using the connection ∇; moreover the map p! depends only on the homotopy class of the path p. This construc...

A classical theorem in complex algebraic geometry states that, for any smooth projective variety, the Gauss map is finite; in particular, a smooth variety and its Gauss image have the same dimension (with the obvious exception of a linear space). Furthermore, even when the variety is not smooth, Zak proved a lower bound on the dimension of its Gauss image in terms of the dimension of its singul...

One of the basic problems for Lie groups is to describe the image of the exponential map. A Lie group H is called exponential resp. weakly exponential if its exponential map is surjective resp. has dense image in H . In this paper we classify all exponential groups which are identity components of almost simple real algebraic groups. The weakly exponential groups of this type were determined in...

The real algebraic set we obtain will in general be singular. The homeomorphism will be piecewise differentiable. Total algebraicity is a very useful concept since it eiliminates many obstructions to making a topological situation algebraic, c.f. [AK1], [AK2], [AK5]. At first glance our result does not seem to be very useful since current algebraic approximation lemmas require nonsingularity. T...

In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.

We give an explicit description of theta-characteristics on tropical curves and characterize the effective ones. construct moduli space, Tgtrop, for genus g as a generalized cone complex. describe fibers specialization map from space Sg, algebraic curves, to Tgtrop.

The concept of weak algebraic hyperstructures or Hv-structures constitutes a generalization of the well-known algebraic hyperstructures (semihypergroup, hypergroup and so on). The overall aim of this paper is to present an introduction to some of the results, methods and ideas about chemical examples of weak algebraic hyperstructures. In this paper after an introduction of basic definitions and...

The automorphism groups of the canonical double covers of the unstable graphs in two infinite families are considered. These graphs are important from the point of view of algebraic map theory as they can be embedded into regular oriented maps.

We prove a version of Schanuel’s Conjecture for a field of Laurent power series in positive characteristic replacing C and a non-algebraic additive power series replacing the exponential map.