Wavefunction topology of two-dimensional time-reversal symmetric superconductors

We discuss the topology of the wavefunctions of two-dimensional time-reversal symmetric superconductors. We consider (a) the planar state, (b) a system with broken up-down reflection symmetry, and (c) a system with general spin-orbit interaction. We show explicitly how the relative sign of the order parameter on the two Fermi surfaces affects this topology, and clarify the meaning of the $Z_2$ classification for these topological states.Comment: only the Introduction has been modified from v

Exactness and maximal automorphic factors of unimodal interval maps

We study exactness and maximal automorphic factors of C^3 unimodal maps of the interval. We show that for a large class of infinitely renormalizable maps, the maximal automorphic factor is an odometer with an ergodic non-singular measure. We give conditions under which maps with absorbing Cantor sets have an irrational rotation on a circle as a maximal automorphic factor, as well as giving exact examples of this type. We also prove that every C^3 S-unimodal map with no attractor is exact with respect to Lebesgue measure. Additional results about measurable attractors in locally compact metric spaces are given

Topology of leaves for minimal laminations by non-simply-connected hyperbolic surfaces

We give the topological obstructions to be a leaf in a minimal lamination by hyperbolic surfaces whose generic leaf is homeomorphic to a Cantor tree. Then, we show that all allowed topological types can be simultaneously embedded in the same lamination. This result, together with results in [arXiv:1906.10029] and [Comment. Math. Helv. 78 (2003), 845–864], completes the panorama of understanding which topological surfaces can be leaves in minimal hyperbolic surface laminations when the topology of the generic leaf is given. In all cases, all possible topologies can be realized simultaneously.ANII:FCE_3_2018_1_14874