The E6 state sum invariant is a topological invariant of closed 3manifolds constructed by using the 6j-symbols of the E6 subfactor. In this paper, we introduce the E6 linear skein as a certain vector space motivated by E6 subfactor planar algebra, and develop its linear skein theory by showing many relations in it. By using this linear skein, we give an elementary self-contained construction of...

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 construct an Alexander-type invariant for oriented doodles from a deformation of the Tits representation twin group and Chebyshev polynomials second kind. Like Alexander polynomial, our vanishes on unlinked with more than one component. also include values several doodles.

BACKGROUND Lessons in the Alexander Technique and exercise prescription proved effective for managing low back pain in primary care in a clinical trial. OBJECTIVES To understand trial participants' expectations and experiences of the Alexander Technique and exercise prescription. METHODS A questionnaire assessing attitudes to the intervention, based on the Theory of Planned Behaviour, was c...

More than 2000 years ago, Alexander the Third of Macedonia conquered the then known world and ruled an empire that extended from the Balkan Peninsula to the Indus River. Alexander changed the course of human history when he sparked the spread of Greek culture throughout the ancient world. Also as the world’s first statesman, he forsaw the advantages of multicultural societies and was clever eno...

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...

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 ...