On connectedness of chaotic sections of some 3-periodic surfaces

Abstract

In the present paper we construct a Z^{3}-periodic surface in R^{3} whose almost all plane sections of a certain direction consist of exactly one connected component. This question originates from a problem of Novikov on the semi- classical motion of an electron in strong magnetic field. Our main tool is the Rips machine algorighm for band complexes.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1010.1820