Uniformly exponential growth and mapping class groups of surfaces

We show that the mapping class group of an orientable finite type surface has uniformly exponential growth, as well as various closely related groups. This provides further evidence that mapping class groups may be linear.Comment: 6 pages, no figure

Empirical pricing kernels obtained from the UK index options market

Empirical pricing kernels for the UK equity market are derived as the ratio between risk-neutral densities, inferred from FTSE 100 index options, and historical real-world densities, estimated from time series of the index. The kernels thus obtained are almost compatible with a risk averse representative agent, unlike similar estimates for the US market

Geodesic axes in the pants complex of the five-holed sphere

AbstractWe study the synthetic geometry of the pants graph of the 5-holed sphere, establishing the existence of geodesics connecting any vertex or ideal point to any ideal point. We prove the existence of geodesic axes for sufficiently high powers of any pseudo-Anosov mapping class, and that large link hierarchies from Harveyʼs curve graph all induce geodesic paths

1995, Spatial and temporal variability of late Neogene equatorial Pacific carbonate

High-resolution, continuous records of GRAPE wet bulk density (a carbonate proxy) from Ocean Drilling Program Leg 138 provide one the opportunity for a detailed study of eastern equatorial Pacific Ocean carbonate sedimentation during the last 6 m.y. The transect of sites drilled spans both latitude and longitude in the eastern equatorial Pacific from 90° to 110°W and from 5°S to 10°N. Two modes of variability are resolved through the use of Empirical Orthogonal Function (EOF) analysis. In the presence of large tectonic and climatic boundary condition changes over the last 6 m.y., the dominant mode of spatial variability in carbonate sedimentation is remarkably constant. The first mode accounts for over 50% of the variance in the data, and is consistent with forcing by equatorial divergence. This mode characterizes both carbonate concentration and carbonate mass accumulation rate time series. Variability in the first mode is highly coherent with insolation, indicating a strong linear relationship between equatorial Pacific car bonate sedimentation and Milankovitch variability. Frequency domain analysis indicates that the coupling to equatorial divergence in carbonate sedimentation is strongest in the precession band (19-23 k.y.) and weakest though present at lower frequencies. The second mode of variability has a consistent spatial pattern of east-west asymmetry over the past 4 m.y. only; prior to 4 Ma, a different mode of spatial variability may have been present, possibly suggesting influence by closure of the Isthmus of Panama or other tectonic changes. The second mode of variability may indicate influence by CaCO3 dissolution. The second mode of variability is not highly coherent with insolation. Comparison of the modes of carbonate variability to a 4 m.y. record of benthic δ 1 8 indicates that although overall correlation between carbonate and δ 1 8 is low, both modes of variability in carbonate sedimentation are coherent with δ 1 8 changes at some frequencies. The first mode of carbonate variability is coherent with Sites 846/849 δ 1 8 at the dominant insolation periods, and the second mode is coherent at 100 k.y. during the last 2 m.y. The coherence between carbonate sedimentation and δ 1 8 in both EOF modes suggests that multiple uncorrelated modes of variability operated within the climate system during the late Neogene