The second bounded cohomology of 3-manifolds
type: Item
instance of: scholarly article
title: The second bounded cohomology of 3-manifolds
zbMATH Open document ID: 1014.57013
author: Koji Fujiwara
author: Ken'ichi Ohshika
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2003-07-01T00:00:00Z
review text: The authors determine the second bounded cohomology of certain 3-manifold groups. By a theorem of Gromov, this yields the singular second bounded cohomology of the corresponding manifolds themselves. More precisely, the authors study those compact orientable 3-manifolds whose fundamental group admits a non-trivial decomposition as an amalgamated product. The main result is that for such groups, the second bounded cohomology is infinite dimensional unless the group is virtually solvable. This result relies among other things on a result of the first author for general amalgamated products [Trans. Am. Math. Soc. 352, No. 3, 1113-1129 (2000; Zbl 1053.20517)]. A more precise statement is given, making use of the structure theory of 3-manifolds without 2-spheres in the boundary. In fact, this more precise statement would be a complete description if Thurston's geometrization conjecture holds.
reviewed by: Nicolas Monod
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 57M07
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 1833279
zbMATH Keywords: bounded cohomology
zbMATH Keywords: 3-manifold groups
zbMATH Keywords: 3-manifolds
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1145476341
OpenAlex ID: W2026097682
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DOI: 10.2977/PRIMS/1145476341
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description: scientific article; zbMATH DE number 1833279