arXiv subjects
Publications and source records attributed to Jonathan Yazinski.
In this note, we describe a procedure to construct generalized complex structures with an arbitrarily large number of type change loci on products of the circle with a connected sum of closed 3-manifolds. The loci need not be isotopic.
The geography of minimal symplectic 4-manifolds with arbitrary fundamental group and symplectic 6-manifolds with abelian fundamental group of small rank, and with arbitrary fundamental group are addressed.
The 3x+1 function T is defined on the positive integers by $T(x) = \frac{3x+1}{2}$ for x odd and $T(x) = \frac{x}{2}$ for x even. The function T has a natural extension to the 2-adic integers, and there is a continuous function $Φ$ which conjugates T to the 2-adic shift map $σ$. Bernstein and Lagarias conjectured that -1 and 1/3 are the only odd fixed points of $Φ$. In this paper we investigate periodicity associated with $Φ$, a property of the map which is a natural extention of solenoidality. We use it to show that there are nontrivial infinite families of 2-adics that are not fixed points of $Φ$. In particular, we prove that three sequences of farPoints of 2-adic integers are finitely pseudoperiodic, providing more evidence supporting the $Φ$ Fixed Point Conjecture.