In the wake of Donaldson’s pioneering work [6], Picard-Lefschetz theory has been extended from its original context in algebraic geometry to (a very large class of) symplectic manifolds. Informally speaking, one can view the theory as analogous to Kirby calculus: one of its basic insights is that one can give a (non-unique) presentation of a symplectic manifold, in terms of a symplectic hypersu...

This paper is the rst part of a program aimed at a better understanding of how the recently de ned Seiberg-Witten-Floer homology for any closed 3-manifold Y with a Spin structure s [7], [12], [18], [20], [35] behaves under surgery. The non-equivariant Seiberg-Witten-Floer homology is constructed from the chain complex generated by the irreducible critical points of the perturbed Chern-Simons-Di...

We prove that the Hochschild homology (and cohomology) of a symmetric open Frobenius algebra A has a natural coBV and BV structure. The underlying coalgebra and algebra structure may not be resp. counital and unital. Moreover we prove that the product and coproduct satisfy the Frobenius compatibility condition i.e. the coproduct on HH∗(A) is a map of left and right HH∗(A)-modules. If A is commu...

This paper deals with topological analysis of sets of tetrahedra (‘‘tetrahedral meshes’’ of three-dimensional objects). We introduce a definition of simple elements for any normal tetrahedral representation. Then we prove a local characterization of simple tetrahedra in the case of a scene composed of one object and its background, based on homology groups and on relative homology. This allows ...

A bacterial strain, Myt-1, was isolated in Toyama Bay in Toyama Prefecture, Japan. Myt-1 was capable of reducing the thalli of various seaweed species to single cell detritus particles. A 16S rDNA homology search revealed that the closest relative of Myt-1 was Saccharophagus degradans 2-40 (CP000282; 100% similarity), which was first isolated in Chesapeake Bay in Virginia, USA. The Myt-1 strain...

Although genes have specific phenotypic consequences in a given species, this functional relationship can clearly change during the course of evolution. Many cases of evolutionary dissociations between homologous genes and homologous morphological features are now known. These dissociations have interesting and important implications for understanding the genetic basis for evolutionary change i...