Departamento de Matemáticas UAM

  • Inicio
  • Inicio (2)
  • Presentación
  • Directorio
  • Organigrama
  • Intranet
  • Convocatoria de plazas
Mes anteior Día anterior
Anual
Mensual
Semanal
Diario
Buscar
Ir al mes específico
Día siguiente Mes siguiente
Anual Mensual Semanal Hoy Buscar Ir al mes específico
SEMINARIO DE TEORÍA DE GRUPOS

SEMINARIO DE TEORÍA DE GRUPOS 

INJECTIVE HOMOMORPHISMS BETWEEN BIG MAPPING CLASS GROUPS <https://www.icmat.es/eventos_web/teoria_grupos/teoria_grupos_20201111010234.pdf>

*Ponente:*Javier Aramayona (ICMAT-CSIC)

*Fecha:*miércoles, 18 de noviembre de 2020 - 11:00

*Lugar:*Online - https://conecta2.csic.es/b/yag-vzv-4gd

*Resumen:*A classical result of Ivanov-McCarthy asserts every injective endomorphism of the mapping class group of a (sufficiently complicated) finite-type surface is induced by a homeomorphism. In particular, mapping class groups of finite-type surfaces are co-Hopfian. In the first part of this talk, we will sketch a proof of this result, and explain why the strategy fails catastrophically for infinite-type surfaces. In the second part, we will in fact construct families of examples of infinite-type surfaces whose (pure) mapping class groups are not co-Hopfian. We will do so by exhibiting several different explicit constructions of injective homomorphisms that are not surjective. In some of these cases, the homomorphisms constructed have further "exotic" dynamical properties. A common feature of our examples is that Dehn twists are sent to products of Dehn twists. For this reason, we will then focus on (not necessarily injective, a priori) homomorphisms that send single Dehn twists to single Dehn twists. We will prove a strong superrigidity result for such homomorphisms: with some extra hypotheses, they are always induced by a homeomorphism between the underlying surfaces. This is joint work with Chris Leininger (Rice) and Alan McLeay (Luxembourg).

Localización SEMINARIO DE TEORÍA DE GRUPOS
CSS Valid | XHTML Valid | Top | + | - | reset
Copyright © Eximium 2025 All rights reserved. Custom Design by Youjoomla.com
Inicio