Construction of infinite finitely presented nill-semigroup

Ilya Ivanov-Pogodayev, Alexey Kanel-Belov

Published 2014-12-16Version 1

The paper deals with the solution of Shevrin problem. Infinite finitely presented nill-semigroup is constructed. The construction is based on aperiodic fillings, Goodman-Strauss type theorems on uniformly elliptic space. Space is called {\it uniformly elliptic} iff there is universal constant $\lambda>0$ such that any two points $A$ and $B$ on distant $D$ can be joined by family of geodesic lines generating a disc of wideness $\lambda\cdot D$. Research was supported by the grant RFBR N 14-01-00548