Practical bounds for a Dehn parental test

Bounds on exceptional Dehn filling

We show that for a hyperbolic knot complement, all but at most 12 Dehn fillings are irreducible with infinite word-hyperbolic fundamental group. AMS Classification numbers Primary: 57M50, 57M27 Secondary: 57M25, 57S25

Bounds on Exceptional Dehn Filling Ii

We show that there are at most finitely many one cusped orientable hyperbolic 3-manifolds which have more than eight non-hyperbolic Dehn fillings. Moreover, we show that determining these finitely many manifolds is decidable.

Quantitative Dengue Test: Is it Practical for Clinical Practice?

Bounds for Test Exponents

Suppose that R is a two-dimensional normal standard-graded domain over a finite field. We prove that there exists a uniform Frobenius test exponent b for the class of homogeneous ideals in R generated by at most n elements. This means that for every ideal I in this class we have that f b ∈ I [p ] if and only if f ∈ I . This gives in particular a finite test for the Frobenius closure. On the oth...

Bounds on Volume Increase Under Dehn Drilling Operations

In this paper we investigate how the volume of hyperbolic manifolds increases under the process of removing a curve, that is, Dehn drilling. If the curve we remove is a geodesic we are able to show that for a certain family of manifolds the volume increase is bounded above by π · l where l is the length of the geodesic drilled. Also we construct examples to show that there is no lower bound to ...