Jump to content
Change search PrimeFaces.cw("Fieldset","widget_formSmash_search",{id:"formSmash:search",widgetVar:"widget_formSmash_search",toggleable:true,collapsed:true,toggleSpeed:500,behaviors:{toggle:function(ext) {PrimeFaces.ab({s:"formSmash:search",e:"toggle",f:"formSmash",p:"formSmash:search"},ext);}}});
$(function(){PrimeFaces.cw("Dialog","citationDialog",{id:"formSmash:upper:j_idt262",widgetVar:"citationDialog",width:"800",height:"600"});});
$(function(){PrimeFaces.cw("ImageSwitch","widget_formSmash_j_idt1632",{id:"formSmash:j_idt1632",widgetVar:"widget_formSmash_j_idt1632",fx:"fade",speed:500,timeout:8000},"imageswitch");});
#### Open Access in DiVA

####

#### Search in DiVA

##### By author/editor

Lindell, Erik
##### By organisation

Department of Mathematics
On the subject

Mathematics
#### Search outside of DiVA

GoogleGoogle Scholar$(function(){PrimeFaces.cw('Chart','widget_formSmash_j_idt1963_0_downloads',{id:'formSmash:j_idt1963:0:downloads',type:'bar',responsive:true,data:[[18,8,12,7,3,1,5]],title:"Downloads of File (FULLTEXT01)",axes:{yaxis: {label:"",min:0,max:30,renderer:$.jqplot.LinearAxisRenderer,tickOptions:{angle:0}},xaxis: {label:"",renderer:$.jqplot.CategoryAxisRenderer,tickOptions:{angle:-90}}},series:[{label:'diva2:1749686'}],ticks:["May -23","Jun -23","Jul -23","Aug -23","Sep -23","Oct -23","Nov -23"],orientation:"vertical",barMargin:6,datatip:true,datatipFormat:"<span style=\"display:none;\">%2$d</span><span>%2$d</span>"},'charts');}); Total: 54 downloads$(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_j_idt1967",{id:"formSmash:j_idt1967",widgetVar:"widget_formSmash_j_idt1967",target:"formSmash:downloadLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade"});}); findCitings = function() {PrimeFaces.ab({s:"formSmash:j_idt1969",f:"formSmash",u:"formSmash:citings",pa:arguments[0]});};$(function() {findCitings();}); $(function(){PrimeFaces.cw('Chart','widget_formSmash_visits',{id:'formSmash:visits',type:'bar',responsive:true,data:[[681,5,2,6,6,4,12]],title:"Visits for this publication",axes:{yaxis: {label:"",min:0,max:690,renderer:$.jqplot.LinearAxisRenderer,tickOptions:{angle:0}},xaxis: {label:"",renderer:$.jqplot.CategoryAxisRenderer,tickOptions:{angle:-90}}},series:[{label:'diva2:1749686'}],ticks:["May -23","Jun -23","Jul -23","Aug -23","Sep -23","Oct -23","Nov -23"],orientation:"vertical",barMargin:6,datatip:true,datatipFormat:"<span style=\"display:none;\">%2$d</span><span>%2$d</span>"},'charts');}); Total: 716 hits
$(function(){PrimeFaces.cw("Dialog","citationDialog",{id:"formSmash:lower:j_idt2075",widgetVar:"citationDialog",width:"800",height:"600"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt221",{id:"formSmash:upper:j_idt221",widgetVar:"widget_formSmash_upper_j_idt221",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt225_j_idt231",{id:"formSmash:upper:j_idt225:j_idt231",widgetVar:"widget_formSmash_upper_j_idt225_j_idt231",target:"formSmash:upper:j_idt225:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Stable invariants of some topological moduli spacesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
2023 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: Department of Mathematics, Stockholm University , 2023. , p. 41
##### Keywords [en]

Moduli spaces, mapping class groups, stable invariants
##### National Category

Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-216273ISBN: 978-91-8014-280-9 (print)ISBN: 978-91-8014-281-6 (electronic)OAI: oai:DiVA.org:su-216273DiVA, id: diva2:1749686
##### Public defence

2023-05-26, lärosal 4, hus 1, Albano, Albanovägen 28, Stockholm, 13:00 (English)
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt728",{id:"formSmash:j_idt728",widgetVar:"widget_formSmash_j_idt728",multiple:true});
##### Supervisors

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt747",{id:"formSmash:j_idt747",widgetVar:"widget_formSmash_j_idt747",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt757",{id:"formSmash:j_idt757",widgetVar:"widget_formSmash_j_idt757",multiple:true}); Available from: 2023-05-03 Created: 2023-04-11 Last updated: 2023-04-24Bibliographically approved
##### List of papers

This thesis consists of three papers, treating stability phenomena in various automorphism groups in topology. In Papers I and III, we study the group (co)homology of certain mapping class groups of surfaces and graphs, or their respective Torelli subgroups, while the subject of Paper II is homotopy automorphisms of higher-dimensional spaces and manifolds.

The subject of Paper I is the rational homology of the Torelli group of a smooth, compact and orientable surface, which is the group of isotopy classes of self-homeomorphisms that act trivially on the first homology group of the surface. Using a map known as the Johnson homomorphism, we compute a large quotient of the rational homology of the Torelli group, in a range where the genus of the surface is sufficiently large in comparison to the homological degree.

In Paper II, we study in parallel pointed homotopy automorphisms of iterated wedge sums of topological spaces and boundary relative homotopy automorphisms of iterated connected sums of manifolds with a disk removed. We prove that the rational homotopy groups of these satisfy something called representation stability for representations of symmetric groups, under some assumptions on the spaces and manifolds, respectively.

In Paper III, we study the cohomology of the automorphism group of the free group F_{n}, which can also be viewed as the mapping class group of a graph of loop order n, with coefficients in tensor products of the first rational homology of F_{n} and its linear dual. In a range where n is sufficiently large compared to the cohomological degree, these cohomology groups are independent of n and the main result of Paper III provides a description of the stable cohomology groups, confirming a conjecture by Djament. These stable cohomology groups are also closely related to the stable cohomology of the Torelli subgroup of the automorphism group of F_{n,} defined similarly as the Torelli group of a surface.

1. Abelian cycles in the homology of the Torelli group$(function(){PrimeFaces.cw("OverlayPanel","overlay1556251",{id:"formSmash:j_idt837:0:j_idt843",widgetVar:"overlay1556251",target:"formSmash:j_idt837:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Representation stability for homotopy automorphisms$(function(){PrimeFaces.cw("OverlayPanel","overlay1556253",{id:"formSmash:j_idt837:1:j_idt843",widgetVar:"overlay1556253",target:"formSmash:j_idt837:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Stable cohomology of Aut(F_{n}) with bivariant twisted coefficients$(function(){PrimeFaces.cw("OverlayPanel","overlay1749679",{id:"formSmash:j_idt837:2:j_idt843",widgetVar:"overlay1749679",target:"formSmash:j_idt837:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

isbn
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1994",{id:"formSmash:j_idt1994",widgetVar:"widget_formSmash_j_idt1994",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt2056",{id:"formSmash:lower:j_idt2056",widgetVar:"widget_formSmash_lower_j_idt2056",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt2057_j_idt2059",{id:"formSmash:lower:j_idt2057:j_idt2059",widgetVar:"widget_formSmash_lower_j_idt2057_j_idt2059",target:"formSmash:lower:j_idt2057:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});