Gusein-Zade's Betti-density conjecture for quasiperiodic functions
Let be a quasiperiodic function, and let denote the density of its -th Betti number at level , defined by averaging the corresponding Betti number over expanding balls when the limit exists. Gusein-Zade's conjecture. For all analytic (respectively, almost all smooth) quasiperiodic functions, the Betti-number densities are well defined. The source explicitly says that this was proved in the smooth case for the Betti-number densities by A. I. Esterov in 2000, so the conjecture is resolved at least in that stated smooth setting.
References
Primary source
Roberto De Leo and Andrei Ya. Maltsev, “Quasiperiodic functions on the plane and electron transport phenomena”, arXiv:1811.10727 (2018).
Additional references
2 papers in this index state this conjecture (2017–2018). The statement above is taken from the most recent of them; the others are arXiv:1711.01716.
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