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Merge trees decoradas e TDA
(Universidade Federal de São Carlos, 2023-08-10)
In this document, first we will introduce Persistance Homology and Category Theory basic concepts. Afterwards, we will develop the Merge Tree Theory which will be useful to keep track of connected components evolution of ...
Categoria de Lusternik-Schnirelmann e aplicações
(Universidade Federal de São Carlos, 2022-02-14)
The Lusternik-Schnirelmann category associates a positive integer to each topological space. This number is an important invariant in algebraic topology, critical point theory and symplectic geometry. In this dissertation ...
Compactly-supported and relative integration in differential cohomology
(Universidade Federal de São Carlos, 2022-04-11)
In this work, we have constructed more general versions of differential integration maps
in differential cohomology theories. Among the obtained versions we can mention the
integration with compact supports, the integration ...