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Hainaut, LouisGadish, Nir
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Department of Mathematics
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Geometry
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Configuration spaces on a wedge of spheres and Hochschild-Pirashvili homologyPrimeFaces.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});
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(English)Manuscript (preprint) (Other academic)
##### Abstract [en]

##### Keywords [en]

Configuration space, Hochschild-Pirashvili homology, polynomial functor
##### National Category

Geometry
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-204141OAI: oai:DiVA.org:su-204141DiVA, id: diva2:1653462
#####

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##### Funder

EU, European Research Council, ERC-2017-STG 759082Available from: 2022-04-21 Created: 2022-04-21 Last updated: 2024-04-25Bibliographically approved
##### In thesis

We study the compactly supported rational cohomology of configuration spaces of points on wedges of spheres, equipped with natural actions of the symmetric group and the group Out(F_g) of outer automorphism of the free group. These representations are closely related to Hochschild-Pirashvili homology with coefficients in square-zero algebras, and they show up in seemingly unrelated parts of mathematics, from cohomology of moduli spaces of curves to polynomial functors on free groups.

We show that these cohomology representations form a polynomial functor, and use various geometric models to compute a substantial part of its composition factors. We further compute the composition factors completely for all configurations of n\leq 10 particles. An application of this analysis is a new super-exponential lower bound on the symmetric group action on the weight 0 component of H^*_c(M_{2,n}).

1. Some computations of compact support cohomology of configuration spaces$(function(){PrimeFaces.cw("OverlayPanel","overlay1653463",{id:"formSmash:j_idt1554:0:j_idt1559",widgetVar:"overlay1653463",target:"formSmash:j_idt1554:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Configuration spaces on a bouquet of spheres and related moduli spaces$(function(){PrimeFaces.cw("OverlayPanel","overlay1854510",{id:"formSmash:j_idt1554:1:j_idt1559",widgetVar:"overlay1854510",target:"formSmash:j_idt1554:1:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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