Latin American Journal of Mathematics

Characterization of Positive Operators

Lucio Fassarella — 2023-05-10

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

Gabriel Bittencourt Rios — 2023-05-11

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

Alcides de Carvalho Junior — 2023-05-29

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

Maico Felipe Silva Ribeiro — 2023-08-13

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

Juliana Roberta Theodoro de Lima — 2023-09-04

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).