Lone Axes in Outer Space

Handel and Mosher define the axis bundle for a fully irreducible outer automorphism in "Axes in Outer Space." In this paper we give a necessary and sufficient condition for the axis bundle to consist of a unique periodic fold line. As a consequence, we give a setting, and means for identifying in this setting, when two elements of an outer automorphism group $Out(F_r)$ have conjugate powers.Comment: Significant revisions for the sake of readability, several arguments filled i

WORLD FOOD PROBLEMS AND PROSPECTS

Food Security and Poverty,

Universal circles for quasigeodesic flows

We show that if M is a hyperbolic 3-manifold which admits a quasigeodesic flow, then pi_1(M) acts faithfully on a universal circle by homeomorphisms, and preserves a pair of invariant laminations of this circle. As a corollary, we show that the Thurston norm can be characterized by quasigeodesic flows, thereby generalizing a theorem of Mosher, and we give the first example of a closed hyperbolic 3-manifold without a quasigeodesic flow, answering a long-standing question of Thurston.Comment: This is the version published by Geometry & Topology on 29 November 2006. V4: typsetting correction

Proliferation versus Differentiation: Redefining Retinoic Acids Role.

Retinoic acid is commonly used in culture to differentiate stem cells into neurons and has established neural differentiation functions in vivo in developing and adult organisms. In this issue of Stem Cell Reports, Mishra et al. (2018) broaden its role in stem cell functions, showing that retinoic acid is necessary for stem and progenitor cell proliferation in the adult brain

Quasi-isometric rigidity for the solvable Baumslag-Solitar groups, II

Let BS(1,n)= . We prove that any finitely-generated group quasi-isometric to BS(1,n) is (up to finite groups) isomorphic to BS(1,n). We also show that any uniform group of quasisimilarities of the real line is bilipschitz conjugate to an affine group.Comment: 42 pages. see also http://www.math.uchicago.edu/~far