Combinatorial and geometric methods in topology

Details Combinatorial and geometric methods in topology Combinatorial and geometric methods in topology

2007-06-29

arxiv.org/abs/0706.4368v1

Milan J. Math. 76 (2008), 69-92

Mathematics

Geometric Topology

This expository paper is the text of a conference given by the author to a broad audience of mathematicians. An upcoming artic

Scientific paper

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 role 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.

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