Revista Integración, temas de matemáticas.
Vol. 29 No. 1 (2011): Revista Integración, temas de matemáticas
Research and Innovation Articles

Introduction to geometric group theory

Olga Salazar-Díaz
Universidad Nacional de Colombia, Escuela de Matemáticas, Medellín, Colombia.
Bio
Gabriel Vergara-Ríos
Universidad de Córdoba, Dpto. de Matemáticas y Estadística, Montería, Colombia
Bio

Published 2011-01-31

Keywords

  • group action,
  • Cayley graphs,
  • quasi-isometries,
  • quasi-isometricembeddings

How to Cite

Salazar-Díaz, O., & Vergara-Ríos, G. (2011). Introduction to geometric group theory. Revista Integración, Temas De matemáticas, 29(1), 15–30. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/2408

Abstract

 In this article we will give an introduction to geometric group theory. We will see how from a finite presentation of a group, we can give this group a metric space structure. We discuss the action of the groupon this space and we study geometric properties preserved under quasiisometry.

Downloads

Download data is not yet available.

References

[1] Bridson M. y Haefliger A., Metric spaces of non-positive curvature, Springer-Verlag, Berlin, 1999.

[2] De la Harpe P., Topics in geometric group theory, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2000.

[3] Geoghegan R., Topological methods in group theory, Graduate Texts in Mathematics, 243, Springer, New York, 2008.

[4] Hatcher A., Algebraic topology, Cambridge University Press, Cambridge, 2002.

[5] Johnson D.L., Presentations of groups, London Mathematical Society Student Texts, 15, Cambridge University Press, Cambridge, 1990.

[6] Lima E.L., Espaços métricos, Projecto Euclides, CNPq, Rio de Janeiro, 2003.