On connectedness of chaotic sections of some 3-periodic surfaces

Details On connectedness of chaotic sections of some 3-periodic surfaces On connectedness of chaotic sections of some 3-periodic surfaces

2011-12-26

arxiv.org/abs/1112.5870v3

Mathematics

Geometric Topology

arXiv admin note: substantial text overlap with arXiv:1010.1820

Scientific paper

In the present paper we construct a triply periodic surface 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
semiclassical motion of an electron in strong magnetic field. Our main tool is
the Rips machine algorighm for band complexes.

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