Satellite operators as group actions on knot concordance

Any knot in a solid torus, called a pattern or satellite operator, acts on knots in the 3-sphere via the satellite construction. We introduce a generalization of satellite operators which form a group (unlike traditional satellite operators), modulo a generalization of concordance. This group has an action on the set of knots in homology spheres, using which we recover the recent result of Cochran and the authors that satellite operators with strong winding number $\pm 1$ give injective functions on topological concordance classes of knots, as well as smooth concordance classes of knots modulo the smooth 4--dimensional Poincare Conjecture. The notion of generalized satellite operators yields a characterization of surjective satellite operators, as well as a sufficient condition for a satellite operator to have an inverse. As a consequence, we are able to construct infinitely many non-trivial satellite operators P such that there is a satellite operator $\overline{P}$ for which $\overline{P}(P(K))$ is concordant to K (topologically as well as smoothly in a potentially exotic $S^3\times [0,1]$) for all knots K; we show that these satellite operators are distinct from all connected-sum operators, even up to concordance, and that they induce bijective functions on topological concordance classes of knots, as well as smooth concordance classes of knots modulo the smooth 4--dimensional Poincare Conjecture.Comment: 20 pages, 9 figures; in the second version, we have added several new results about surjectivity of satellite operators, and inverses of satellite operators, and the exposition and structure of the paper have been improve

Concordance of knots in S1×S2S^1\times S^2

We establish a number of results about smooth and topological concordance of knots in $S^1\times S^2$. The winding number of a knot in $S^1\times S^2$ is defined to be its class in $H_1(S^1\times S^2;\mathbb{Z})\cong \mathbb{Z}$. We show that there is a unique smooth concordance class of knots with winding number one. This improves the corresponding result of Friedl-Nagel-Orson-Powell in the topological category. We say a knot in $S^1\times S^2$ is slice (resp. topologically slice) if it bounds a smooth (resp. locally flat) disk in $D^2\times S^2$. We show that there are infinitely many topological concordance classes of non-slice knots, and moreover, for any winding number other than $\pm 1$, there are infinitely many topological concordance classes even within the collection of slice knots. Additionally we demonstrate the distinction between the smooth and topological categories by constructing infinite families of slice knots that are topologically but not smoothly concordant, as well as non-slice knots that are topologically slice and topologically concordant, but not smoothly concordant.Comment: 25 pages, 19 figures, final version, to appear in Journal of London Mathematical Societ

A comparison of geocoding baselayers for electronic medical record data analysis

Indiana University-Purdue University Indianapolis (IUPUI)Identifying spatial and temporal patterns of disease occurrence by mapping the residential locations of affected people can provide information that informs response by public health practitioners and improves understanding in epidemiological research. A common method of locating patients at the individual level is geocoding residential addresses stored in electronic medical records (EMRs) using address matching procedures in a geographic information system (GIS). While the process of geocoding is becoming more common in public health studies, few researchers take the time to examine the effects of using different address databases on match rate and positional accuracy of the geocoded results. This research examined and compared accuracy and match rate resulting from four commonly-used geocoding databases applied to sample of 59,341 subjects residing in and around Marion County/ Indianapolis, IN. The results are intended to inform researchers on the benefits and downsides to their selection of a database to geocode patient addresses in EMRs

Annealing effect of hybrid solar cells based on poly (3-hexylthiophene) and zinc-oxide nanostructures

The structural growth and optical and photovoltaic properties of the organic–inorganic hybrid structures of zinc oxide (ZnO)-nanorods/poly-3-hexylthiophene (P3HT) and two variations of organic polymer blends of ZnO/ P3HT:C60 fullerene and ZnO/P3HT:6,6]-phenyl C61 butyric acid methyl ester were studied in detail during thermal annealing. The ordering of the P3HT nanocrystals increased during annealing, which also improved hole transport in the hybrid structures. The optical constants of the ZnO/P3HT:[6,6]-phenyl C61 butyric acid methyl ester (PCBM) films elevated with annealing temperature due to the improved crystallisation induced by the formation of P3HT crystalline domains. As a result, a maximum power conversion efficiency of approximately 1.03% was achieved for the annealed ZnO/P3HT:PCBM device at 140 °C. These findings indicate that ZnO-nanorods/P3HT:PCBM films are stable at temperatures up to 160 °C.Web of Scienc

Small volume laboratory on a chip measurements incorporating the quartz crystal microbalance to measure the viscosity-density product of room temperature ionic liquids

A microfluidic glass chip system incorporating a quartz crystal microbalance (QCM) to measure the square root of the viscosity-density product of room temperature ionic liquids (RTILs) is presented. The QCM covers a central recess on a glass chip, with a seal formed by tightly clamping from above outside the sensing region. The change in resonant frequency of the QCM allows for the determination of the square root viscosity-density product of RTILs to a limit of ∼ 10 kg m−2 s−0.5. This method has reduced the sample size needed for characterization from 1.5 ml to only 30 μl and allows the measurement to be made in an enclosed system