Abstract.
Starting from the (apparently) elementary problem of deciding how many different topological spaces can be obtained by gluing together in pairs the faces of an octahedron, we will describe the central rôle played by hyperbolic geometry within three-dimensional topology. We will also point out the striking difference with the two dimensional case, and we will review some of the results of the combinatorial and computational approach to three-manifolds developed by different mathematicians over the last several years.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Lecture held by Carlo Petronio in the Seminario Matematico e Fisico di Milano on April 23, 2007
Rights and permissions
About this article
Cite this article
Petronio, C., Heard, D. & Pervova, E. Combinatorial and Geometric Methods in Topology. Milan j. math. 76, 69–92 (2008). https://doi.org/10.1007/s00032-007-0080-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00032-007-0080-x