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2012 Lagrangian mapping class groups from a group homological point of view
Takuya Sakasai
Algebr. Geom. Topol. 12(1): 267-291 (2012). DOI: 10.2140/agt.2012.12.267


We focus on two kinds of infinite index subgroups of the mapping class group of a surface associated with a Lagrangian submodule of the first homology of a surface. These subgroups, called Lagrangian mapping class groups, are known to play important roles in the interaction between the mapping class group and finite-type invariants of 3–manifolds. In this paper, we discuss these groups from a group (co)homological point of view. The results include the determination of their abelianizations, lower bounds of the second homology and remarks on the (co)homology of higher degrees. As a byproduct of this investigation, we determine the second homology of the mapping class group of a surface of genus 3.


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Takuya Sakasai. "Lagrangian mapping class groups from a group homological point of view." Algebr. Geom. Topol. 12 (1) 267 - 291, 2012.


Received: 20 November 2010; Revised: 1 November 2011; Accepted: 10 November 2011; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1262.55006
MathSciNet: MR2916276
Digital Object Identifier: 10.2140/agt.2012.12.267

Primary: 55R40
Secondary: 32G15 , 57R20

Keywords: Lagrangian filtration , mapping class group , Miller–Morita–Mumford class , Torelli group

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.12 • No. 1 • 2012
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