Lagrangian mapping class groups from a group homological point of view
type: Item
instance of: scholarly article
title: Lagrangian mapping class groups from a group homological point of view
zbMATH Open document ID: 1262.55006
author: Takuya Sakasai
published in: Algebraic \& Geometric Topology
publication date: 2012-05-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/0910.5262
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 57M99
zbMATH DE Number: 6035477
zbMATH Keywords: mapping class group
zbMATH Keywords: Torelli group
zbMATH Keywords: Lagrangian filtration
zbMATH Keywords: Miller-Morita-Mumford class
reviewed by: Mahan Mj
MaRDI profile type: Publication
OpenAlex ID: W3103137681
arXiv ID: 0910.5262
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DOI: 10.2140/AGT.2012.12.267
review text: The author studies certain infinite index subgroups of the mapping class group associated to Lagrangian submodules of the first homology group of a surface. The point of view is that of group cohomology. Let \(H = H_1(\Sigma)\) be the first homology group of a closed surface. Let \(L\) be a Lagrangian submodule of \(H\) with respect to the intersection bilinear form. Let NEWLINE\[NEWLINE{\mathcal L}_g = \{ f \in {\mathcal M}_g : f_\ast (L)= L \}.NEWLINE\]NEWLINE NEWLINE\[NEWLINE{\mathcal{I L}}_g = \{ f \in {\mathcal M}_g : f_\ast|_L= id_L \}.NEWLINE\]NEWLINENEWLINENEWLINEIn the paper under review the author computes the following:NEWLINENEWLINE1) \(H_1({\mathcal{I L}}_g)\)NEWLINENEWLINE2) \(H_1({\mathcal{L}}_g/{\mathcal{I}}_g)\)NEWLINENEWLINE3) \(H_2({\mathcal{L}}_g/{\mathcal{I}}_g)\)NEWLINENEWLINE4) \(H_1({\mathcal{L}}_g)\) NEWLINENEWLINE5) a lower bound on \(H_2({\mathcal{L}}_g)\).
description: scientific article; zbMATH DE number 6035477