We show that a random walk on the mapping class group of an orientable surface of finite type makes linear progress in the relative metric, which is quasi-isometric to the complex of curves.
The HMG-I gene family encodes high mobility group proteins originally identified as nonhistone chromosomal binding proteins. HMG-I and -Y proteins are alternatively spliced products of the same mRNA; HMG-C is encoded by a separate gene. The HMG-I proteins function as architectural chromatin-binding proteins that bind to the narrow groove of AT-rich regions… (More)
We show that a random walk on the mapping class group of an orientable surface gives rise to a pseudo-Anosov element with asymptotic probability one. Our methods apply to many subgroups of the mapping class group, including the Torelli group.
Consider a random walk on the mapping class group, and let wn be the location of the random walk at time n. A random Heegaard splitting M (wn) is a 3-manifold obtained by using wn as the gluing map between two handlebodies. We show that the joint distribution of (wn, w −1 n) is asymptotically independent, and converges to the product of the harmonic and… (More)
We show that for certain hyperbolic manifolds all boundary slopes are slopes of π 1-injective immersed surfaces, covered by incompressible embeddings in some finite cover. The manifolds include hyperbolic punctured torus bundles and hyperbolic two-bridge knots.
T T T T T T T T T T T T T T T Abstract We show that a free period three action on the three-sphere is standard, ie, the quotient is homeomorphic to a lens space. We use a minimax argument involving sweepouts.
INTRODUCTION Multiple distinct tumors arising in a single individual or within members of a family raise the suspicion of a genetic susceptibility disorder. CASE PRESENTATION We present the case of a 52-year-old Caucasian woman diagnosed with sebaceous gland carcinoma of the eyelid, followed several years later with subsequent diagnoses of breast cancer… (More)
We show that if a closed hyperbolic 3-manifold has a sequence of finite covers of bounded Heegaard genus, then it is virtually fibered. This generalizes a theorem of Lackenby, removing restrictions needed about the regularity of the covers. Furthermore, we can replace the assumption that the covers have bounded Heegaard genus with the weaker hypotheses that… (More)
Genotyping experiments are widely used in clinical and basic research laboratories to identify associations between genetic variations and normal/abnormal phenotypes. Genotyping assay techniques vary from single genomic regions that are interrogated using PCR reactions to high throughput assays examining genome-wide sequence and structural variation. The… (More)