Abelian and non-abelian cohomology
Algebraic Geometry
2014-04-22 v1
Abstract
We place the representation variety in the broader context of abelian and nonabelian cohomology. We outline the equivalent constructions of the moduli spaces of flat bundles, of smooth integrable connections, and of holomorphic integrable connections over a compact Kaehler manifold. In addition, we describe the moduli space of Higgs bundles and how it relates to the representation variety. We attempt to avoid abstraction, but strive to present and clarify the unifying ideas underlying the theory.
Keywords
Cite
@article{arxiv.1404.5025,
title = {Abelian and non-abelian cohomology},
author = {Eugene Z. Xia},
journal= {arXiv preprint arXiv:1404.5025},
year = {2014}
}
Comments
39 pages. Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore: Volume 23, Geometry, Topology And Dynamics Of Character Varieties, 2012 Geometry, Topology And Dynamics Of Character Varieties