The Poincaré conjecture. Clay research conference, resolution of the Poincaré conjecture, Institut Henri Poincaré, Paris, France, June 8--9, 2010
type: Item
instance of: scholarly article
zbMATH Open document ID: 1300.57002
publication date: 2014-11-13T00:00:00Z
Mathematics Subject Classification ID: 57-06
Mathematics Subject Classification ID: 57M40
Mathematics Subject Classification ID: 57-03
Mathematics Subject Classification ID: 53-06
Mathematics Subject Classification ID: 53C44
Mathematics Subject Classification ID: 53-03
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 00B25
zbMATH DE Number: 6369114
MaRDI profile type: Publication
title: The Poincaré conjecture. Clay research conference, resolution of the Poincaré conjecture, Institut Henri Poincaré, Paris, France, June 8--9, 2010
published in: Clay Mathematics Proceedings
review text: This volume contains seven papers based on the Clay Research Conference held at the Institut Henri Poincaré in Paris, in 2010, to celebrate the resolution of Poincaré conjecture. The articles are of expository nature and cover several subjects around geometry and topology of low dimensional manifolds. They are not bound to the resolution of the conjecture and all together provide a broad view of the geometry and topology of manifolds, since Poincaré's time to the current open questions. The volume starts with M. Aliyah's contribution ``Geometry in 2, 3 and 4 dimensions'', which is a brief introduction to geometric low dimensional manifolds.NEWLINENEWLINENEWLINENEWLINENext comes the paper by \textit{J. W. Morgan} entitled [``100 Years of Topology: Work Stimulated by Poincaré's Approach to Classifying Manifolds'', Clay Math. Proc. 19, 7--29 (2014; Zbl 1304.55001)]. As the title explains, it describes how the work of Poincaré influenced many generations of topologists, and how the study of manifolds has evolved during 100 years. It starts with a detailed description of Poincaré's Analysis Situs and its complements, it discusses several developements duringt the 20th Century, and finishes with modern developments in low dimensional topology, where ideas from physics, geometry and analysis appear.NEWLINENEWLINENEWLINENEWLINEThe third contribution is by \textit{C. T. McMullen}: [``The Evolution of Geometric Structures on 3-Manifolds'', Bull. Am. Math. Soc., New Ser. 48, No. 2, 259--274 (2011; Zbl 1214.57017)]. The best description is given by the author himself: ``This article--based on a lecture at that conference--aims to give a brief and impressionistic introduction to the geometrization conjecture: its historical precedents, the approaches to its resolution, and some of the remaining open questions.''NEWLINENEWLINENEWLINENEWLINEThe paper ``Invariants of Manifolds of the Classification Problem'' by \textit{S. K. Donaldson} [Clay Math. Proc. 19, 47--63 (2014; Zbl 1304.5…
reviewed by: Joan Porti
description: scientific article; zbMATH DE number 6369114