The Asymptotic Cone of Teichm\"uller Space: Thickness and Divergence

We study the Asymptotic Cone of Teichm\"uller space equipped with the Weil-Petersson metric. In particular, we provide a characterization of the canonical finest pieces in the tree-graded structure of the asymptotic cone of Teichm\"uller space along the same lines as a similar characterization for right angled Artin groups by Behrstock-Charney and for mapping class groups by Behrstock-Kleiner-Minksy-Mosher. As a corollary of the characterization, we complete the thickness classification of Teichm\"uller spaces for all surfaces of finite type, thereby answering questions of Behrstock-Drutu, Behrstock-Drutu-Mosher, and Brock-Masur. In particular, we prove that Teichm\"uller space of the genus two surface with one boundary component (or puncture) can be uniquely characterized in the following two senses: it is thick of order two, and it has superquadratic yet at most cubic divergence. In addition, we characterize strongly contracting quasi-geodesics in Teichm\"uller space, generalizing results of Brock-Masur-Minsky. As a tool, we develop a complex of separating multicurves, which may be of independent interest.Comment: This paper comprises the main portion of the author's doctoral thesis, 54 page

Relationship between education, health and crime: fable, fallacy or fact

The study is an empirical evaluation of specific criminal activities. The relationship of criminal activities with inflation, unemployment, investment, education and health are examined through an annual data set from 1980 to 2007. To test the order of integration, Augmented Dickey Fuller test and Philips Perron are used. To find the evidences of long run relationship, Cointegrating Regression Durban Watson, Engle Granger two step procedure and Johansen and Juselis method is used. Results show that education and health have a positive and significant relationship with most of the criminal activities in the study. Another unusual finding is that inflation and unemployment are insignificant in case of two out of three crimes, however, investment is found highly significant and negatively related with these crimes. The study indicates that an educated, healthy and legally employed person can also be involved in unsophisticated blue collar criminal activities.Education; health; Crime