Paysage Systolique Des Surfaces Hyperboliques Compactes De Caracteristique -1
Abstract
We determine optimal inequalities for the systole of all hyperbolic compact surfaces of caracteristic -1. First, we study the geometry and topology of these surfaces. Then, we describe the action of modular groups on Teichm\"uller spaces. Finaly, we give cell decompositions of fundamental domains such as the set of systoles is constant over a cell. Other optimal inequalities for other metric invariants are also given.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.