Commensurations of the Johnson kernel

Let K be the subgroup of the extended mapping class group, Mod(S), generated by Dehn twists about separating curves. Assuming that S is a closed, orientable surface of genus at least 4, we confirm a conjecture of Farb that Comm(K), Aut(K) and Mod(S) are all isomorphic. More generally, we show that any injection of a finite index subgroup of K into the Torelli group I of S is induced by a homeomorphism. In particular, this proves that K is co-Hopfian and is characteristic in I. Further, we recover the result of Farb and Ivanov that any injection of a finite index subgroup of I into I is induced by a homeomorphism. Our method is to reformulate these group theoretic statements in terms of maps of curve complexes.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper37.abs.htm

Tempering Our Expectations: Drinking, Smoking, and the Economy of a Western Massachusetts Farmstead-Tavern

Between 1800 and 1830, William Sanford and his family operated a tavern in Hawley, a hilltown in western Massachusetts. The establishment was located on the town’s common, adjacent to the community’s Congregational meetinghouse and several other taverns. At the initiative of the local historical preservation group the Sons and Daughters of Hawley, archaeologists, students, teachers, and community members excavated the tavern site between 2011 and 2014. Historical and archaeological research indicates that William Sanford’s homestead functioned not only as a tavern, but also as a farm, store, smithy, and occasionally a court of law. Material evidence of alcohol and tobacco consumption, however, is less pronounced than at heavily-trafficked urban taverns. Research at the Sanford Tavern and other 19th-century public houses indicates that hybrid rural establishments played a variety of social and economic roles within local communities, which is evident in the archaeological record. Our findings show that archaeologists should approach rural farmstead-taverns with a different set of expectations

Accidental parabolics and relatively hyperbolic groups

By constructing, in the relative case, objects analoguous to Rips and Sela's canonical representatives, we prove that the set of images by morphisms without accidental parabolic, of a finitely presented group in a relatively hyperbolic group, is finite, up to conjugacy.Comment: Revision, 24 pages, 4 figure

Ergodic directions for billiards in a strip with periodically located obstacles

We study the size of the set of ergodic directions for the directional billiard flows on the infinite band $\R\times [0,h]$ with periodically placed linear barriers of length $0<\lambda<h$. We prove that the set of ergodic directions is always uncountable. Moreover, if $\lambda/h\in(0,1)$ is rational the Hausdorff dimension of the set of ergodic directions is greater than 1/2. In both cases (rational and irrational) we construct explicitly some sets of ergodic directions.Comment: The article is complementary to arXiv:1109.458

Triangulations and volume form on moduli spaces of flat surfaces

In this paper, we are interested in flat metric structures with conical singularities on surfaces which are obtained by deforming translation surface structures. The moduli space of such flat metric structures can be viewed as some deformation of the moduli space of translation surfaces. Using geodesic triangulations, we define a volume form on this moduli space, and show that, in the well-known cases, this volume form agrees with usual ones, up to a multiplicative constant.Comment: 42 page

HEMATOLOGICAL ANALYSIS OF THE HEALTH STATUS OF THE BAIKAL OMUL IN THE SPAWNING SEASON AGAINST INVASION DIPHYLLOBOTHRIUM DENDRITICUM (CESTODA: PSEUDOPHYLLIDAE)

Based on original research we attempted to assess the range of hematological parameters of the hemopoietic system in the Baikal omul infected. D. dendriticum in the spawning period. The following effects were found: low functional activity of T-cell immunity, constant level of B-cell immunity; the intensification of erythropoiesis; cellular responses give evidences of endogenous intoxication. Overall, identified hematologic changes as in infected as in uninfected subjects of the Baikal omul proceeded were in adaptive criterias

Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow

We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates.Comment: Minor corrections. To appear in Publications mathematiques de l'IHE

Periodic Orbits and Spectral Statistics of Pseudointegrable Billiards

We demonstrate for a generic pseudointegrable billiard that the number of periodic orbit families with length less than $l$ increases as $\pi b_0l^2/\langle a(l) \rangle$, where $b_0$ is a constant and $\langle a(l) \rangle$ is the average area occupied by these families. We also find that $\langle a(l) \rangle$ increases with $l$ before saturating. Finally, we show that periodic orbits provide a good estimate of spectral correlations in the corresponding quantum spectrum and thus conclude that diffraction effects are not as significant in such studies.Comment: 13 pages in RevTex including 5 figure