胞腔复形上的希格斯束和有限生成群的表示
Higgs bundles over cell complexes and representations of finitely generated groups
摘要：
本文将Donaldson-Corlette定理推广到胞腔复形上向量丛的情形。我们定义了复形上的向量丛和Higgs丛的概念，并描述了相应的Betti、de Rham和Higgs模空间.主要定理是：一个可容许群$Γ$的$SL(r, \mathbb{C})$特征标簇与具有$π_1(X) = Γ$的可容许复$X$上秩$r$ Higgs丛的模空间同胚.定义在奇异域上的调和映射理论起着关键作用。
英文摘要：
The purpose of this paper is to extend the Donaldson-Corlette theorem to the case of vector bundles over cell complexes. We define the notion of a vector bundle and a Higgs bundle over a complex, and describe the associated Betti, de Rham and Higgs moduli spaces. The main theorem is that the $SL(r, \mathbb{C})$ character variety of a finitely presented group $Γ$ is homeomorphic to the moduli space of rank $r$ Higgs bundles over an admissible complex $X$ with $π_1(X) = Γ$. A key role is played by the theory of harmonic maps defined on singular domains.
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