The top homology group of the genus 3 Torelli group

The Torelli group of a genus oriented surface is the subgroup of the mapping class group consisting of all mapping classes that act trivially on . The quotient group is isomorphic to the symplectic group . The cohomological dimension of the group equals to . The main goal of the present paper is to...

Full description

Saved in:
Bibliographic Details
Published in:Journal of topology 2023-09, Vol.16 (3), p.1048-1092
Main Author: Spiridonov, Igor A.
Format: Article
Language:English
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c190t-878405f7d5b4fb3773ec6a860dfd38aba2b5e49758a8c8ec9c69803a3a9a91853
container_end_page 1092
container_issue 3
container_start_page 1048
container_title Journal of topology
container_volume 16
creator Spiridonov, Igor A.
description The Torelli group of a genus oriented surface is the subgroup of the mapping class group consisting of all mapping classes that act trivially on . The quotient group is isomorphic to the symplectic group . The cohomological dimension of the group equals to . The main goal of the present paper is to compute the top homology group of the Torelli group in the case as ‐module. We prove an isomorphism where is the quotient of by its diagonal subgroup with the natural action of the permutation group (the action of is trivial). We also construct an explicit set of generators and relations for the group .
doi_str_mv 10.1112/topo.12308
format article
fullrecord <record><control><sourceid>crossref</sourceid><recordid>TN_cdi_crossref_primary_10_1112_topo_12308</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1112_topo_12308</sourcerecordid><originalsourceid>FETCH-LOGICAL-c190t-878405f7d5b4fb3773ec6a860dfd38aba2b5e49758a8c8ec9c69803a3a9a91853</originalsourceid><addsrcrecordid>eNo9j81KAzEYRYNYsNZufIKshanJfPn5spTiHxTcjOuQySTTytQMyXTRt7e14upeONwLh5B7zlac8_pxSmNa8RoYXpE51xIqFLW4_u9c3ZDbUr4YUzUDNSfQbAM9reg27dOQ-iPtczqMNEU6nUgfvg-FAm1SDsOwu8A7MotuKGH5lwvy-fLcrN-qzcfr-_ppU3lu2FShRsFk1J1sRWxBawheOVSsix2ga13dyiCMlujQY_DGK4MMHDjjDEcJC_Jw-fU5lZJDtGPe7V0-Ws7sWdeede2vLvwAo65H2Q</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>The top homology group of the genus 3 Torelli group</title><source>Wiley-Blackwell Read &amp; Publish Collection</source><creator>Spiridonov, Igor A.</creator><creatorcontrib>Spiridonov, Igor A.</creatorcontrib><description>The Torelli group of a genus oriented surface is the subgroup of the mapping class group consisting of all mapping classes that act trivially on . The quotient group is isomorphic to the symplectic group . The cohomological dimension of the group equals to . The main goal of the present paper is to compute the top homology group of the Torelli group in the case as ‐module. We prove an isomorphism where is the quotient of by its diagonal subgroup with the natural action of the permutation group (the action of is trivial). We also construct an explicit set of generators and relations for the group .</description><identifier>ISSN: 1753-8416</identifier><identifier>EISSN: 1753-8424</identifier><identifier>DOI: 10.1112/topo.12308</identifier><language>eng</language><ispartof>Journal of topology, 2023-09, Vol.16 (3), p.1048-1092</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c190t-878405f7d5b4fb3773ec6a860dfd38aba2b5e49758a8c8ec9c69803a3a9a91853</cites><orcidid>0000-0003-1351-4169</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Spiridonov, Igor A.</creatorcontrib><title>The top homology group of the genus 3 Torelli group</title><title>Journal of topology</title><description>The Torelli group of a genus oriented surface is the subgroup of the mapping class group consisting of all mapping classes that act trivially on . The quotient group is isomorphic to the symplectic group . The cohomological dimension of the group equals to . The main goal of the present paper is to compute the top homology group of the Torelli group in the case as ‐module. We prove an isomorphism where is the quotient of by its diagonal subgroup with the natural action of the permutation group (the action of is trivial). We also construct an explicit set of generators and relations for the group .</description><issn>1753-8416</issn><issn>1753-8424</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNo9j81KAzEYRYNYsNZufIKshanJfPn5spTiHxTcjOuQySTTytQMyXTRt7e14upeONwLh5B7zlac8_pxSmNa8RoYXpE51xIqFLW4_u9c3ZDbUr4YUzUDNSfQbAM9reg27dOQ-iPtczqMNEU6nUgfvg-FAm1SDsOwu8A7MotuKGH5lwvy-fLcrN-qzcfr-_ppU3lu2FShRsFk1J1sRWxBawheOVSsix2ga13dyiCMlujQY_DGK4MMHDjjDEcJC_Jw-fU5lZJDtGPe7V0-Ws7sWdeede2vLvwAo65H2Q</recordid><startdate>202309</startdate><enddate>202309</enddate><creator>Spiridonov, Igor A.</creator><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-1351-4169</orcidid></search><sort><creationdate>202309</creationdate><title>The top homology group of the genus 3 Torelli group</title><author>Spiridonov, Igor A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c190t-878405f7d5b4fb3773ec6a860dfd38aba2b5e49758a8c8ec9c69803a3a9a91853</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Spiridonov, Igor A.</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of topology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Spiridonov, Igor A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The top homology group of the genus 3 Torelli group</atitle><jtitle>Journal of topology</jtitle><date>2023-09</date><risdate>2023</risdate><volume>16</volume><issue>3</issue><spage>1048</spage><epage>1092</epage><pages>1048-1092</pages><issn>1753-8416</issn><eissn>1753-8424</eissn><abstract>The Torelli group of a genus oriented surface is the subgroup of the mapping class group consisting of all mapping classes that act trivially on . The quotient group is isomorphic to the symplectic group . The cohomological dimension of the group equals to . The main goal of the present paper is to compute the top homology group of the Torelli group in the case as ‐module. We prove an isomorphism where is the quotient of by its diagonal subgroup with the natural action of the permutation group (the action of is trivial). We also construct an explicit set of generators and relations for the group .</abstract><doi>10.1112/topo.12308</doi><tpages>45</tpages><orcidid>https://orcid.org/0000-0003-1351-4169</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 1753-8416
ispartof Journal of topology, 2023-09, Vol.16 (3), p.1048-1092
issn 1753-8416
1753-8424
language eng
recordid cdi_crossref_primary_10_1112_topo_12308
source Wiley-Blackwell Read & Publish Collection
title The top homology group of the genus 3 Torelli group
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-06T23%3A14%3A43IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20top%20homology%20group%20of%20the%20genus%203%20Torelli%20group&rft.jtitle=Journal%20of%20topology&rft.au=Spiridonov,%20Igor%20A.&rft.date=2023-09&rft.volume=16&rft.issue=3&rft.spage=1048&rft.epage=1092&rft.pages=1048-1092&rft.issn=1753-8416&rft.eissn=1753-8424&rft_id=info:doi/10.1112/topo.12308&rft_dat=%3Ccrossref%3E10_1112_topo_12308%3C/crossref%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c190t-878405f7d5b4fb3773ec6a860dfd38aba2b5e49758a8c8ec9c69803a3a9a91853%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true