Actions of SL(n,Z) on homology spheres

Any continuous action of SL(n,Z), where n > 2, on a r-dimensional mod 2 homology sphere factors through a finite group action if r < n - 1. In particular, any continuous action of SL(n+2,Z) on the n-dimensional sphere factors through a finite group action.Comment: 11 page

Coronal loop oscillations and diagnostics with Hinode/EIS

Context.Standing slow (acoustic) waves commonly observed in hot coronal loops offer a unique opportunity to understand the properties of the coronal plasma. The lack of evidence for similar oscillations in cooler loops is still a puzzle. Aims.The high cadence EIS instrument on board recently launched Hinode has the capability to detect wave motion in EUV lines both in the imaging and spectroscopy modes. The paper aims to establish the distinct characteristics of standing and propagating acoustic waves and to predict their footprints in EIS data. Methods.A 1D hydrodynamic loop model is used and the consequences of various types of heating pulses are examined. In each case, the resulting hydrodynamic evolution of the loop is converted into observables using a selection of available EIS spectral lines and windows. Results.Propagating/standing acoustic waves are a natural response of the loop plasma to impulsive heating. Synthetic EIS observations of such waves are presented both in the imaging and spectroscopy modes. The waves are best seen and identified in spectroscopy mode observations. It is shown that the intensity oscillations, unlike the Doppler shift oscillations, continuously suffer phase shifts due to heating and cooling of the plasma. It is therefore important to beware of this effect when interpreting the nature of the observed waves

Simple braids for surface homeomorphisms

Let S be a compact, oriented surface with negative Euler characteristic and let f be a homeomorphism of S that is isotopic to the identity. If there exists a periodic orbit with a non-zero rotation vector, then there exists a simple braid with the same rotation vector.Comment: 12 pages, 2 figure

On 3-manifolds that support partially hyperbolic diffeomorphisms

Let M be a closed 3-manifold that supports a partially hyperbolic diffeomorphism f. If $\pi_1(M)$ is nilpotent, the induced action of f on $H_1(M, R)$ is partially hyperbolic. If $\pi_1(M)$ is almost nilpotent or if $\pi_1(M)$ has subexponential growth, M is finitely covered by a circle bundle over the torus. If $\pi_1(M)$ is almost solvable, M is finitely covered by a torus bundle over the circle. Furthermore, there exist infinitely many hyperbolic 3-manifolds that do not support dynamically coherent partially hyperbolic diffeomorphisms; this list includes the Weeks manifold. If f is a strong partially hyperbolic diffeomorphism on a closed 3-manifold M and if $\pi_1(M)$ is nilpotent, then the lifts of the stable and unstable foliations are quasi-isometric in the universal of M. It then follows that f is dynamically coherent. We also provide a sufficient condition for dynamical coherence in any dimension. If f is center bunched and if the center-stable and center-unstable distributions are Lipschitz, then the partially hyperbolic diffeomorphism f must be dynamically coherent.Comment: 21 page

Six simple guidelines for introducing new genera of fungi

We formulate five guidelines for introducing new genera, plus one recommendation how to publish the results of scientific research. We recommend that reviewers and editors adhere to these guidelines. We propose that the underlying research is solid, and that the results and the final solutions are properly discussed. The six criteria are: (1) all genera that are recognized should be monophyletic; (2) the coverage of the phylogenetic tree should be wide in number of species, geographic coverage, and type species of the genera under study; (3) the branching of the phylogenetic trees has to have sufficient statistical support; (4) different options for the translation of the phylogenetic tree into a formal classification should be discussed and the final decision justified; (5) the phylogenetic evidence should be based on more than one gene; and (6) all supporting evidence and background information should be included in the publication in which the new taxa are proposed, and this publication should be peer-reviewed

Monotone periodic orbits for torus homeomorphisms

Let f be a homeomorphism of the torus isotopic to the identity and suppose that there exists a periodic orbit with a non-zero rotation vector (p/q,r/q), then f has a topologically monotone periodic orbit with the same rotation vector.Comment: 10 pages, 1 figur

Commutators as Powers in Free Products of Groups

The ways in which a nontrivial commutator can be a proper power in a free product of groups are identified.Comment: AMS-LaTex, 6 pages, no figure

Symmetric random walks on Homeo+(R)

We study symmetric random walks on finitely generated groups of orientation-preserving homeomorphisms of the real line. We establish an oscillation property for the induced Markov chain on the line that implies a weak form of recurrence. Except for a few special cases, which can be treated separately, we prove a property of "global stability at a finite distance": roughly speaking, there exists a compact interval such that any two trajectories get closer and closer whenever one of them returns to the compact interval. The probabilistic techniques employed here lead to interesting results for the study of group actions on the line. For instance, we show that under a suitable change of the coordinates, the drift of every point becomes zero provided that the action is minimal. As a byproduct, we recover the fact that every finitely generated group of homeomorphisms of the real line is topologically conjugate to a group of (globally) Lipschitz homeomorphisms. Moreover, we show that such a conjugacy may be chosen in such a way that the displacement of each element is uniformly bounded

Situating Our Rhetorical Practice

As the writing consultants and Assistant Director have demonstrated, kairos is a core concept that we can use productively to situate and reflect on our rhetorical practice. The idea of “right timing,” the “opportune moment,” and the “embodiment of carpe diem” will further help us push past the false dualism of either directive or nondirective tutoring (Hawhee 20) . As the reflections above show, enacting kairotic thinking in the writing center can move us beyond that either-or choice and perhaps move us towards a stronger both-and philosophy. Since consultants are creative individuals who make important decisions on the spot when working with complicated individuals, this core concept invites us to reflect on our practices and our principles. Hill describes kairos as a “habit of mind, one that expresses itself in a kind of time that is living and creative” (212). The creativity of writing consultants brings to life the possibilities explored in Geller’s discussion of “epochal time” and coheres with the call put forth by the authors of The Everyday Writing Center that “[a]t the very heart of what we five have come to understand as we’ve talked about time is our belief that writing centers should be most focused on time that is relational” (33). Tutoring with kairos in mind provides a way to conceptualize that relational model of writing center practice.University Writing Cente

Zero entropy subgroups of mapping class groups

Let $M$ be a compact surface with boundary. We are interested in the question of how a group action on $M$ permutes a finite invariant set $X \subset int(M)$. More precisely, how the algebraic properties of the induced group of permutations of a finite invariant set affects the dynamical properties of the group. Our main result shows that in many circumstances if the induced permutation group is not solvable then among the homeomorphisms in the group there must be one with a pseudo-Anosov component. We formulate this in terms of the mapping class group relative to the finite set and show the stronger result that in many circumstances (e.g. if $\partial M \ne \emptyset$) this mapping class group is itself solvable if it has no elements with pseudo-Anosov components