Geometric invariants for 3-manifolds
type: Item
instance of: scholarly article
title: Geometric invariants for 3-manifolds
zbMATH Open document ID: 0751.57001
DOI: 10.1007/BF03024140
author: Robert Meyerhoff
published in: The Mathematical Intelligencer
publication date: 1992-09-27T00:00:00Z
review text: This is a pleasant and reasonable short and non-technical introduction to the topology and geometry of 2- and 3-dimensional manifolds, recommendable to everyone (in particular, non-specialists) who wants to learn about basic facts and ideas as well as some recent developments in this growing field, which has seen such an enormous progress in the last 20 years developing connections with various other fields of mathematics. First, the classification and recognition problem for 2-manifolds is discussed, with the Euler characteristic as the basic invariant, as well as hyperbolic 2-manifolds. The paper then passes to 3-manifolds, especially hyperbolic 3-manifolds and the effectiveness of their invariants: homology, volume, the Chern-Simons and the \(\eta\)-invariant. Here the article becomes an interesting mixture between basic constructions and recent results and problems.
Mathematics Subject Classification ID: 57-02
Mathematics Subject Classification ID: 57-01
Mathematics Subject Classification ID: 57M50
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 58235
zbMATH Keywords: eta invariant
zbMATH Keywords: introduction to the topology and geometry of 2- and 3- dimensional manifolds
zbMATH Keywords: classification and recognition of 2-manifolds
zbMATH Keywords: hyperbolic 2-manifolds
zbMATH Keywords: hyperbolic 3-manifolds
zbMATH Keywords: homology
zbMATH Keywords: volume
zbMATH Keywords: Chern- Simons invariant
reviewed by: Bruno Zimmermann
describes a project that uses: SnapPea
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 58235