Flat fully augmented links are determined by their complements

In this paper, we show that two flat fully augmented links with homeomorphic complements must be equivalent as links in $\mathbb{S}^{3}$. This requires a careful analysis of how totally geodesic surfaces and cusps intersect in these link complements and behave under homeomorphism. One consequence of this analysis is a complete classification of flat fully augmented link complements that admit multiple reflection surfaces. In addition, our work classifies those symmetries of flat fully augmented link complements which are not induced by symmetries of the corresponding link.Comment: 52 pages, 22 figure

The Cyclic Cutwidth of QnQ_n

In this article the cyclic cutwidth of the $n$-dimensional cube is explored. It has been conjectured by Dr. Chavez and Dr. Trapp that the cyclic cutwidth of $Q_n$ is minimized with the Graycode numbering. Several results have been found toward the proof of this conjecture.Comment: 8 pages, 3 figures. Summer Research Experiences for Undergraduates report from August 2003, with some typos fixe

GeoGebra Activities: Tracing Points

In this activity, we will learn how to use GeoGebra (www.geogebra.org) to trace the movement of points, which depend on the movement of other objects. The paths of these points determine curves and we will provide algebraic descriptions of these curves

Belted sum decompositions of fully augmented links

Given two orientable, cusped hyperbolic 3-manifolds containing certain thrice-punctured spheres, Adams gave a diagrammatic definition for a third such manifold, their belted sum. Fully augmented links, or FALs, are hyperbolic links constructed by augmenting a link diagram. This work considers belted sum decompositions in which all manifolds involved are FAL complements. To do so, we provide explicit classifications of thrice punctured spheres in FAL complements, making them easily recognizable. These classifications are used to characterize belted sum prime FALs geometrically, combinatorially and diagrammatically. Finally we prove that, in the context of belted sums, every FAL complement canonically decomposes into FALs which are either prime or two-fold covers of the Whitehead link

A linear representation of the mapping class group and the theory of winding numbers

This paper describes a linear representation F of the mapping class group , of an orientable surface S with one boundary component. The representation F extends the symplectic representation, and is defined for surfaces of arbitrary genus g> 1. The main tools used to define F are crossed homomorphisms which are defined using nonvanishing vector fields X on S, and the theory of winding numbers of curves on surfaces described by Chillingworth in [1,2]. These crossed homomorphisms were essentially described by Morita in [6]. A geometric interpretation of F is then given. If T1S denotes the unit tangent bundle of S1 then F records the action of on H1(T1S;Z). The kernel of F is then characterized using knowledge of the crossed homomorphisms ex. If matrix entries are taken modulo 2g-2, the representation F factors through the mapping class group of a closed orientable surface of genus g > 1. Thus F induces representations of Dn of for any n[-45 degree rule]2g-2. The Dn were discovered by Sipe in [7, 8], and it is noted that her characterization of the image of Dn carries over to the integer valued case. The structure found in characterizing ker F is then used to study ker Dn. In particular, it is shown that a uotient of ker Dn is a semidirect product for each even n dividing 2g-2.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30247/1/0000642.pd

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

Meeting abstrac