Quantization of complex Lagrangian submanifolds

Let Λ be a smooth Lagrangian submanifold of a complex symplectic manifold X. We construct twisted simple holonomic modules along Λ in the stack of deformation-quantization modules on X.     

Analysis of X（1576） as a Tetraquark State with the QCD Sum Rules

We take the viewpoint that X（1576） is the tetraquark state which consists of a scalar diquark and an antiscalar-diquark in relative P-wave, and calculate its mass in the framework of the QCD sum rule approach. The numerical value of the mass mx= （1.66 =k 0.14） GeV is consistent with the experimental data. There might be some tetraquark components in the vector meson X（1576）.     

Separable subgroups of mapping class groups

We investigate separability questions for the mapping class group of a surface. While this group is not subgroup separable in general, we prove a large family of interesting subgroups are separable. This includes many classically studied subgroups such as solvable subgroups, Heegaard and Handlebody groups, geometric subgroups, and all the terms in the Johnson filtration.     

Note on a conjecture of toft

A conjecture of Toft [17] asserts that any 4-critical graph (or equivalently, every 4-chromatic graph) contains a fully odd subdivision ofK ₄. We show that if a graphG has a degree three nodev such thatG-v is 3-colourable, then eitherG is 3-colourable or it contains a fully oddK ₄. This resolves Toft's conjecture in the special case where a 4-critical graph has a degree three node, which is in turn used to prove the conjecture for line-graphs. The proof is constructive and yields a polynomial algorithm which given a 3-degenerate graph either finds a 3-colouring or exhibits a subgraph that is a fully odd subdivision ofK ₄. (A graph is 3-degenerate if every subgraph has some node of degree at most three.)     

Cycles throughk vertices in bipartite tournaments

We give a simple proof that everyk-connected bipartite tournament has a cycle through every set ofk vertices. This was conjectured in [4].This research was done while the first author was visiting Laboratoire de Recherche en Informatique, universite Paris-Sud whose hospitality and financial support is gratefully acknowledged     

Optimal Domains for <Emphasis Type="Italic">L</Emphasis><Superscript>0</Superscript>-valued Operators Via Stochastic Measures

We study extension of operators T: E→ L⁰([0, 1]), where E is an F–function space and L⁰([0, 1]) the space of measurable functions with the topology of convergence in measure, to domains larger than E, and we study the properties of such domains. The main tool is the integration of scalar functions with respect to stochastic measures and the corresponding spaces of integrable functions. Partially supported by D.G.I. #MTM2006-13000-C03-01 (Spain).     

Solving the Gleason problem on linearly convex domains

Let be a bounded, connected linearly convex set in with boundary. We show that the maximal ideal (both in ) and ) consisting of all functions vanishing at is generated by the coordinate functions . Received: 2 July 2001; in final form: 26 September 2001 / Published online: 28 February 2002     

Microlocal study of topological Radon transforms and real projective duality

Various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of (subanalytically) constructible sheaves developed by Kashiwara [M. Kashiwara, Index theorem for constructible sheaves, Astérisque 130 (1985) 193-209] and Kashiwara-Schapira [M. Kashiwara, P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin-Heidelberg-New York, 1990]. In particular, we prove in the real setting some results similar to the ones proved by Ernström in the complex case [L. Ernström, Topological Radon transforms and the local Euler obstruction, Duke Math. J. 76 (1994) 1-21]. For this purpose, we describe the characteristic cycles of topological Radon transforms of constructible functions in terms of curvatures of strata in real projective spaces.     

Sobolev Spaces with only Trivial Isometries

We will give some conditions for Sobolev spaces on bounded Lipschitz domains to admit only trivial isometries.