Surgery formulae for finite type invariants of rational homology 3--spheres

We first present three graphic surgery formulae for the degree $n$ part $Z_n$ of the Kontsevich-Kuperberg-Thurston universal finite type invariant of rational homology spheres. Each of these three formulae determines an alternate sum of the form $$\sum_{I \subset N} (-1)^{\sharp I}Z_n(M_I)$$ where $N$ is the set of components of a framed algebraically split link $L$ in a rational homology sphere $M$, and $M_I$ denotes the manifold resulting from the Dehn surgeries on the components of $I$. The first formula treats the case when $L$ is a boundary link with $n$ components, while the second one is for $3n$--component algebraically split links. In the third formula, the link $L$ has $2n$ components and the Milnor triple linking numbers of its 3--component sublinks vanish. The presented formulae are then applied to the study of the variation of $Z_n$ under a $p/q$-surgery on a knot $K$. This variation is a degree $n$ polynomial in $q/p$ when the class of $q/p$ in \QQ/\ZZ is fixed, and the coefficients of these polynomials are knot invariants, for which various topological properties or topological definitions are given.Comment: 51 pages, uses pstrick

Gardes à vue, 48h du polar à Clermont-Ferrand

Les festivals thématiques autour du polar se sont multipliés ces dernières années. Pourquoi et comment naît une telle manifestation, quels sont les ingrédients d’une recette réussie

La bibliothèque en 8 questions…

« Paint it black ! » Quatre auteurs du noir ont répondu à notre enquête qui, pour l’occasion, a étendu son périmètre pour accueillir un grand auteur américain. De la Mazarine à la Phillips County Library (Helena, Arkansas), en passant par la BM de Tournon-sur-Rhône, les bibliothèques sont « chéries noires »

The Level-0 Muon Trigger for the LHCb Experiment

A very compact architecture has been developed for the first level Muon Trigger of the LHCb experiment that processes 40 millions of proton-proton collisions per second. For each collision, it receives 3.2 kBytes of data and it finds straight tracks within a 1.2 microseconds latency. The trigger implementation is massively parallel, pipelined and fully synchronous with the LHC clock. It relies on 248 high density Field Programable Gate arrays and on the massive use of multigigabit serial link transceivers embedded inside FPGAs.Comment: 33 pages, 16 figures, submitted to NIM