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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.
The object of this expository work is to try to unveil the topological/geometric intuition behind the theory of free groups and their automorphism and outer automorphism groups. The method we follow is to focus on a series of problems in the study of
Traditional classifications of crystalline phases focus on nuclear degrees of freedom. Through examination of both electronic and nuclear structure, we introduce the concept of an electronic plastic crystal. Such a material is classified by crystalli
We study the loxodromic elements for the action of $Out(F_n)$ on the free splitting complex of the rank $n$ free group $F_n$. We prove that each outer automorphism is either loxodromic, or has bounded orbits without any periodic point, or has a perio
Antimony sulfide (Sb2S3) and selenide (Sb2Se3) have emerged as promising earth-abundant alternatives among thin-film photovoltaic compounds. A distinguishing feature of these materials is their anisotropic crystal structures, which are composed of qu
While solar power systems have offered a wide variety of electricity generation approaches including photovoltaics, solar thermal power systems, and solar thermoelectric generators, the ability of generating electricity at both the daytime and nightt