We present a twisted version of the Alexander polynomial associated with a matrix representation of the knot group. Examples of two knots with the same Alexander module but different twisted Alexander polynomials are given.

Taiwanese species of the crane fly subgenus Antocha (Antocha) Osten Sacken, 1860, are reviewed. Antocha (Antocha) taiwanensis, new species, is described and figured. Previously known species, Antocha (A.) bifida Alexander, 1924a and Antocha (A.) styx Alexander, 1930 are redescribed and illustrated. Antocha (A.) javanensis Alexander, 1915 is removed from the list of Taiwanese crane flies. Antoch...

We prove that the LMO-invariant of a 3-manifold of rank one is determined by the Alexander polynomial of the manifold, and conversely, that the Alexander polynomial is determined by the LMO-invariant. Furthermore, we show that the Alexander polynomial of a null-homologous knot in a rational homology 3-sphere can be obtained by composing the weight system of the Alexander polynomial with the Årh...

Davis showed that the topological concordance class of a link in the 3-sphere is uniquely determined by its Alexander polynomial for 2-component links with Alexander polynomial one. A similar result for knots with Alexander polynomial one was shown earlier by Freedman. We prove that these two cases are the only exceptional cases, by showing that the link concordance class is not determined by t...

We show that some of the main results in Laurentiu Maxim’s paper [10] can be obtained (even in a slightly more general setting) using the theory of perverse sheaves of finite rank over Q as described for instance in author’s recent book [3].

Alexander Fleming (18811955) After Louis Pasteur's and Robert Koch's publications on the germ theory of disease, doctors developed a better understanding of the cause of infection. However, methods of treatment were still limited to vaccinations and anti-toxins. Joseph Lister's carbolic spray worked with some success during operations, but was not suitable for everyday use. The question was, ho...

What follows is a summary of a recent paper by Berchtold and Hausen [BH03] in which the language of bunches applied to toric varieties is presented and investigated. I would like to thank Jaros law Wísniewski for drawing this paper to my attention and helping me appreciate the methods described. In order to motivate the definitions, we first present an example in which the weighted projected sp...

Using recent results of the second author which explicitly identify the “(1, 2, 1, 2)avoiding” GL(p,C)×GL(q,C)-orbit closures on the flag manifold GL(p+q,C)/B as certain Richardson varieties, we give combinatorial criteria for determining smoothness, lci-ness, and Gorensteinness of such orbit closures. (In the case of smoothness, this gives a new proof of a theorem of W.M. McGovern.) Going a st...

James Alexander Thomson [4], affectionately known as Jamie Thomson [4], is an American developmental biologist whose pioneering work in isolating and culturing non-human primate [5] and human embryonic stem cells [6] has made him one of the most prominent scientists in stem cell research. While growing up in Oak Park, Illinois, Thomson?s rocket-scientist uncle inspired him to pursue science as ...

Metal-Organic Framework Materials Omar K. Farha,† Alexander M. Spokoyny,† Karen L. Mulfort,†,‡ M. Frederick Hawthorne,§ Chad A. Mirkin,*,† and Joseph T. Hupp*,† Department of Chemistry and International Institute for Nanotechnology, Northwestern UniVersity, 2145 Sheridan Road, EVanston, Illinois 60208, Chemistry DiVision, Argonne National Laboratory, Argonne, Illinois 60439, and International I...