Noncommutative complex differential geometry
Algebraic Geometry
2013-03-07 v2 Differential Geometry
Quantum Algebra
Abstract
This paper defines and examines the basic properties of noncommutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a differential structure on a noncommutative algebra defined in terms of a differential graded algebra. This is compared to current ideas on noncommutative algebraic geometry.
Cite
@article{arxiv.1209.3595,
title = {Noncommutative complex differential geometry},
author = {Edwin Beggs and S. Paul Smith},
journal= {arXiv preprint arXiv:1209.3595},
year = {2013}
}
Comments
42 pages. A few small changes and corrections to the previous version after being refereed. To appear in the special issue of the Journal for Geometry and Physics for the meeting "Noncommutative Algebraic Geometry and its Applications to Physics" 19-23 March 2012, Leiden NL