Consider genus g curves that admit degree d covers to an elliptic curve simply branched at 2g − 2 points. Vary a branch point and the locus of such covers forms a one-parameter family W . We investigate the geometry of W by using admissible covers to study its slope, genus and components. The results can also be applied to study slopes of effective divisors on the moduli space of genus g curves.

Using a result of Tian concerning deformation of negatively curved metrics to Einstein metrics, we conclude that, for any fixed link with hyperbolic complement, there is a class of irregular branched covering spaces, branched over that link, effectively detectable by their branching indices, which consists entirely of closed hyperbolic manifolds. Section 0 Introduction. One of the elusive compo...

We show that several torsion free 3-manifold groups are not left-orderable. Our examples are groups of cyclic branched covers of S branched along links. The figure eight knot provides simple nontrivial examples. The groups arising in these examples are known as Fibonacci groups which we show not to be left-orderable. Many other examples of non-orderable groups are obtained by taking 3-fold bran...

Abstract We compute the gap distribution of directions saddle connections for two classes translation surfaces. One class will be surfaces arising from gluing identical tori along a slit. These yield first explicit computations distributions non-lattice show that this has support at zero and quadratic tail decay. also construct examples in any genus $d>1$ have same as glued The second we con...

Forty disposable medical shoe covers were briefly exposed to the surgical floor and were found contaminated by a large number of bacteria. This study also demonstrated live bacteria, including pathogens attached to contaminated shoe covers, can be subsequently transferred to surgical bedsheets. We suggest an infection control policy should be considered to prevent patients returning to their be...