ar X iv : m at h / 03 10 11 1 v 1 [ m at h . G T ] 8 O ct 2 00 3 On Kontsevich Integral of torus knots ∗

ar X iv : m at h / 03 10 27 4 v 1 [ m at h . A P ] 1 7 O ct 2 00 3 THE RADIATION FIELD IS A FOURIER INTEGRAL OPERATOR

ar X iv : m at h / 03 10 29 5 v 1 [ m at h . D G ] 1 8 O ct 2 00 3 Isomorphisms of algebras of smooth functions revisited ∗

A short proof of the fact that isomorphisms between algebras of smooth functions on Hausdorff smooth manifolds are implemented by diffeomorphisms is given. It is not required that manifolds are second countable or paracompact. This solves a problem stated by A. Wienstein. Some related results are discussed as well.

ar X iv : h ep - l at / 0 11 00 06 v 2 3 O ct 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : m at h / 99 02 05 8 v 1 [ m at h . G T ] 8 F eb 1 99 9 The limit configuration space integral for tangles and the Kontsevich integral

This article is the continuation of our first article (math/9901028). It shows how the zero-anomaly result of Yang implies the equality between the configuration space integral and the Kontsevich integral.

ar X iv : m at h / 02 10 17 4 v 1 [ m at h . G T ] 1 1 O ct 2 00 2 GENERATING FUNCTIONS , FIBONACCI NUMBERS AND RATIONAL KNOTS

We describe rational knots with any of the possible combinations of the properties (a)chirality, (non-)positivity, (non-)fiberedness, and unknotting number one (or higher), and determine exactly their number for a given number of crossings in terms of their generating functions. We show in particular how Fibonacci numbers occur in the enumeration of fibered achiral and unknotting number one rat...