Combinatorial and Geometric Methods in Topology

Autor:	Carlo Petronio, Damian Heard, Ekaterina Pervova
Rok vydání:	2007
Předmět:	Mathematics - Geometric Topology Octahedron General Mathematics Hyperbolic geometry FOS: Mathematics Geometric Topology (math.GT) Point (geometry) Topological space Topology 57M50 Topology (chemistry) Mathematics
Zdroj:	Milan Journal of Mathematics. 76:69-92
ISSN:	1424-9294 1424-9286
DOI:	10.1007/s00032-007-0080-x
Popis:	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. Comment: This expository paper is the text of a conference given by the author to a broad audience of mathematicians. An upcoming article will contain more detailed proofs and an accurate description of the hyperbolic and non-hyperbolic orientable manifolds obtained by gluing together in pairs the faces of the octahedron. Appendix by Damian Heard and Ekaterina Pervova
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2169d9d8d2dce87d6d6cc3b7422acca4 https://doi.org/10.1007/s00032-007-0080-x Zobrazit plný text záznamu Full text from SpringerLink