Casson's invariant for homology 3-spheres and characteristic classes of surface bundles. I
type: Item
instance of: scholarly article
title: Casson's invariant for homology 3-spheres and characteristic classes of surface bundles. I
zbMATH Open document ID: 0684.57008
DOI: 10.1016/0040-9383(89)90011-6
author: Shigeyuki Morita
published in: Topology
publication date: 1989-01-01T00:00:00Z
review text: This is a profound study of the relationship between the Casson invariant of a homology-3-sphere and the structure of certain subgroups of the mapping-class group of a closed surface related to the Torelli group, i.e. the subgroup of mapping classes acting trivially on the homology of the surface (and giving rise, via Heegaard splittings, to homology 3- spheres). It makes use of D. Johnson's study of the Torelli group and an interpretation of the Casson invariant as a secondary invariant associated with the characteristic classes of surface bundles over surfaces. An integer-valued function on the mapping-class group is defined, and the main result of the paper states that its restriction to the subgroup of the Torelli group generated by twists along bounding simple-closed curves (which is sufficient to construct, via Heegaard splittings, all homology-3-spheres) is essentially Casson's invariant of the corresponding homology-3-spheres.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 57R50
Mathematics Subject Classification ID: 57N05
zbMATH DE Number: 4121037
zbMATH Keywords: Casson invariant of a homology-3-sphere
zbMATH Keywords: subgroups of the mapping-class group of a closed surface
zbMATH Keywords: Torelli group
zbMATH Keywords: characteristic classes of surface bundles over surfaces
reviewed by: Bruno Zimmermann
MaRDI profile type: Publication
full work available at URL: 0040-9383(89)90011-6
OpenAlex ID: W2077261144
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description: scientific article; zbMATH DE number 4121037