Latin American Journal of Mathematics

Lists of Editors

2024-02-27T00:23:30+00:00

Characterization of Positive Operators

2023-03-13T14:46:23+00:00

A characterization of positive operators on finite dimensional complex vector spaces, developed from the Routh-Hurwitz criterion with review of some basic concepts and results.

Model Theory Inspired by Modern Algebraic Geometry

2023-01-26T13:22:10+00:00

In this survey, we expound sheaf representations of categories in the context of categorical logic. Namely, we present classifying topoi of coherent theories in terms of equivariant sheaves of groupoid (and then explore the generalization of this technique to a more general categorical context); expose a representation of Grothendieck topoi as global sections of sheaf and, finally, show a quick introduction to logical schemes, a proposed model-theoretic analogue to the schemes of Algebraic Geometry.

A remark on the fundamental group of a compact negatively curved manifold

2023-03-01T19:43:14+00:00

In this expository article we review some results about the fundamental group of a compact negatively curved manifold. In particular, a theorem of Gusevskij, see [7], it states that the fundamental group of a compact negatively curved manifold does not belong to C, where C is the smallest class of groups that contains all amenable groups and is closed under free products and finite extensions. The class C is quite natural and was introduced for the first time in [8].

Poincar´e duality and the existence of exotic structures on n-spheres

2023-05-08T22:06:31+00:00

Poincar´e duality is a remarkable result in Algebraic Topology. It guarantees the existence of an isomorphism between the homology and cohomology groups of manifolds. We present a survey of the most general version of this result and its most important variations such as the Lefschetz duality and the Alexander duality. We consider an important application of these results in the study of the existence of exotic structures on n-spheres.

An exact sequence for generalized string links over surfaces

2023-08-29T16:37:17+00:00

In this work we extend Goldberg result [4] for generalized string links over closed, connected and orientable surfaces of genus $g \geq 1$, i.e., different from the sphere (up to link-homotopy).