Decorated Local Systems and Character Varieties
Benedetta Facciotti, Marta Mazzocco, Nikita Nikolaev

TL;DR
This paper develops a categorical framework to unify various approaches to the decorated Betti moduli space of local systems and character varieties on surfaces, especially with irregular singularities and higher order poles.
Contribution
It introduces a systematic categorical framework that coherently relates different existing descriptions of decorated Betti moduli spaces with irregular singularities.
Findings
Unified description of moduli spaces of local systems and character varieties.
Framework captures irregular singularities and higher order poles.
Establishes connections between various existing approaches.
Abstract
The focus of this paper is the study of the moduli space of representations of fundamental groupoids of surfaces with boundaries with values in . In absence of marked points on the boundary, this moduli space is realized in many equivalent ways: as the moduli space of linear local systems on , as the moduli space of representations of the fundamental groupoid , as the space of monodromy data and as character variety. By adding marked points to the boundary of in order to capture irregular singularities, the Betti moduli space has been generalized in several ways by many authors. Although it is clear that these different approaches describe essentially the same spaces of mathematical objects, exactly how they fit together has not yet been established. Motivated by the broader programme of establishing an explicit and…
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Polynomial and algebraic computation
