Has experience in Mathematics, focusing on algebraic and differential topologies. (Source: Lattes Curriculum)
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The main aim of this project consists in the construction of a natural differential extension of singular homology, dualizing the analogous extension in the framework of cohomology. In particular, the groups we are going to define are supposed to fit in suitable exact sequences, analogous to the cohomological ones. Moreover, we expect that the corresponding version of Poincaré duality hol…
The candidate intends to deepen his knowledge on K-theory, considering its various significant versions and their main applications. Moreover, he is going to analyse in detail the construction of the most relevant models of twisted K-theory. In particular, he will concentrate on the model through twisted vector bundles, trying to show directly that it represents a twisted cohomology theor…
The candidate, during his previous bachelor projects, learnt the basic concepts of Algebraic Topology (fundamental group and covering spaces, singular homology and cohomology, first notions about generalized cohomology theories). In this project we are going to study the language of $\infty$-categories, which is essential to understand the classification of topological field theories achi…
During the first six months, the student will learn about singular homology and cohomology theories, in order to complete his knowledge about basic algebraic topology. Then we will start the study of topological K-theory and we will show explicitly that it is a generalized cohomological theory that obeys all the axioms of Eilenberg-Steenrod, except for the dimension one. (AU)
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The present project is the natural continuation of the one realized by the former Ph.D. student Alffer Gustavo Hernandez Posada, who computed some interesting twisted K-theory groups up to extension, i.e. he showed that they are the central term of a certain short exact sequence. This is a meaningful result, but it has to be completed by computing the groups themselves, not only up to ext…
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