Uniformizing Dessins and Belyi Maps Via Circle Packing - Brossura

Bowers, Philip L.; Stephenson, Kenneth

Brossura

ISBN 10: 0821835238 ISBN 13: 9780821835234

Casa editrice: Amer Mathematical Society, 2004

Riassunto

Grothendieck's theory of Dessins d'Enfants involves combinatorially determined affine, reflective, and conformal structures on compact surfaces. In this paper the authors establish the first general method for uniformizing these dessin surfaces and for approximating their associated Belyi meromorphic functions. The paper begins by developing a discrete theory of dessins based on circle packing. This theory is surprisingly faithful, even at its coarsest stages, to the geometry of the classical theory, and it displays some new sources of richness; in particular, algrebraic number fields enter the theory in a new way. Furthermore, the discrete dessin structures converge to their classical counterparts under a hexagonal refinement scheme.Since the discrete objects are computable, circle packing provides opportunities both for routine experimentation and for large scale explicit computation, as illustrated by a variety of dessin examples up to genus 4 which are computed and displayed. The paper goes on to discuss uses of discrete conformal geometry with triangulations arising in other situations, such as conformal tilings and discrete meromorphic functions. It concludes by addressing technical and implementation issues and open mathematical questions that they raise.

Dettagli dell?edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2004
• ISBN 10: 0821835238
• ISBN 13: 9780821835234
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 97
• Contatto del produttore: non disponibile