On character varieties of singular manifolds

In this paper, we construct a lax monoidal Topological Quantum Field Theory that computes virtual classes, in the Grothendieck ring of algebraic varieties, of G-representation varieties over manifolds with conic singularities, which we will call nodefolds. This construction is valid for any algebrai...

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Detalhes bibliográficos
Autores: Logares Jiménez, Marina Lucía, González Prieto, José Ángel
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/7232
Acesso em linha:https://hdl.handle.net/20.500.14352/7232
Access Level:acceso abierto
Palavra-chave:515.17
Cone sigularities
Character variety
TQFT
Grothendieck ring
Topología
1210 Topología
Descrição
Resumo:In this paper, we construct a lax monoidal Topological Quantum Field Theory that computes virtual classes, in the Grothendieck ring of algebraic varieties, of G-representation varieties over manifolds with conic singularities, which we will call nodefolds. This construction is valid for any algebraic group G, in any dimension and also in the parabolic setting. In particular, this TQFT allow us to compute the virtual classes of representation varieties over complex singular planar curves. In addition, in the case G = SL2(k), the virtual class of the associated character variety over a nodal closed orientable surface is computed both in the non-parabolic and in the parabolic scenarios.