Non-compact Hopf maps, quantum Hall effect, and twistor theory

摘要

Introducing a non-compact version of the Hopf maps, we develop a non-compact, formulation of the quantum Hall effect. In particular, we focus on a construction of quantum Hall effect, on a 4D hyperboloid. It is pointed that the non-compact 4D quantum Hall effect shares remarkably analogous structures with twistor theory. The contents are based on the recent papers arXiv:0902.2523 and arXiv:0905.2792.