Book Reviews by Cleiton Ricardo
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Papers by Cleiton Ricardo
Universidade Federal da Paraíba, Jul 31, 2014
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The geometry of the simplicial complexes was under-investigated before the beginning of the last ... more The geometry of the simplicial complexes was under-investigated before the beginning of the last decade, but since then there seems to have been an explosion of work in this field. Therefore, new structures come to emerge with the development and discoveries within the framework of simplicial geometry. In this thesis, we push forward the development of the theory of energized simplicial complexes, a structure derived from abstract simplicial complexes that behaves as a generalization of their classical topological version. In addition to an introduction to this new structure, we studied the first energized operators, the development of the energized Gauss-Bonnet and Poincare-Hopf theorems, the energized Denh-Sommerville relations, and a discrete version of the Rieman-Roch theorem. The thesis also presents a selection of strategies and pathways to develop further results within the structure of energized simplicial complexes. These new results for which the strategies are drawn can b...
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Book Reviews by Cleiton Ricardo
Papers by Cleiton Ricardo