Grafs i superfícies de Riemann

Abstract

[en] This memory presents basic notions and results about Riemann surfaces which are later seen applied in an analogous way in graphs. The analogy is given in divisors’ context, enunciating a version for graphs of the known Riemann-Roch Theorem. In addition, other results analogous to classical facts about Riemann surfaces theory are shown and proved, like the jacobian or the Abel-Jacobi map. Finally, the analogy with divisors is used for observing a possible application on a Chip-Firing game, a graphs’ game, making it possible to characterise the existence or non-existence of a winning strategy.