Latin American Journal of Mathematics <p>The Latin American Journal of Mathematics <em>(ISSN 2965-0798)</em>, with a continuous submission flow, publishes articles derived from original research and also articles of scientific dissemination in pure and applied mathematics. Graduate students are encouraged to submit articles based on their master's or doctoral thesis.</p> <p>The journal accepts papers preferably in English but also accepts papers in Spanish and Portuguese, employs a double-blind review process, and is aimed at researchers, educators, and students both nationally and internationally.</p> <p>The Latin American Journal of Mathematics supports free access to scientific knowledge, and is free of cost for both readers and authors.</p> <p>The Latin American Journal of Mathematics is published under the Open Access model and adheres to the terms of the Creative Commons Attribution (CC-BY) license, available at <a href="" target="_blank" rel="noopener" data-saferedirecturl=";source=gmail&amp;ust=1542191446547000&amp;usg=AFQjCNF8-uFJACarUVLvfT8ozdN5zvTcDw"></a>.</p> Universidade Federal de São Carlos en-US Latin American Journal of Mathematics 2965-0798 <p> </p> <p>Authors may enter into separate non-commercial contractual agreements for the non-exclusive distribution of the journal's published version of the work (for example, posting it in an institutional repository or publishing it in a book), with an acknowledgment of its initial publication in this journal.</p> Lists of Editors Leandro de Oliveira Copyright (c) 2024 Leandro Nery de Oliveira 2024-02-27 2024-02-27 2 01 Characterization of Positive Operators <p>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.</p> Lucio Fassarella Copyright (c) 2023 Lucio Fassarella 2023-05-10 2023-05-10 2 01 1 11 Model Theory Inspired by Modern Algebraic Geometry <p>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.</p> Gabriel Bittencourt Rios Hugo Luiz Mariano Copyright (c) 2023 Gabriel Bittencourt Rios, Hugo Luiz Mariano 2023-05-11 2023-05-11 2 01 12 50 A remark on the fundamental group of a compact negatively curved manifold <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>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].</p> </div> </div> </div> <pre><br /><br /><br /></pre> <p> </p> Alcides de Carvalho Junior Copyright (c) 2023 Alcides de Carvalho Junior 2023-05-29 2023-05-29 2 01 51 57 Poincar´e duality and the existence of exotic structures on n-spheres <p>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.</p> Maico Felipe Silva Ribeiro Leandro Nery de Oliveira Thiago Filipe da Silva Copyright (c) 2023 Maico Felipe Silva Ribeiro, Leandro Nery de Oliveira, Thiago Filipe da Silva 2023-08-13 2023-08-13 2 01 58 98 An exact sequence for generalized string links over surfaces <p>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).</p> Juliana Roberta Theodoro de Lima Copyright (c) 2023 Juliana Roberta Theodoro de Lima 2023-09-04 2023-09-04 2 01 99 112