Lantern relations and rational blowdowns

Generalized symplectic rational blowdowns

We prove that the generalized rational blowdown, a surgery on smooth 4-manifolds, can be performed in the symplectic category. AMS Classi cation 57R17; 57R15, 57M50

Symplectic Rational Blowdowns

We prove that the rational blowdown, a surgery on smooth 4-manifolds introduced by Fintushel and Stern, can be performed in the symplectic category. As a consequence, interesting families of smooth 4-manifolds, including the exotic K3 surfaces of Gompf and Mrowka, admit symplectic structures. A basic problem in symplectic topology is to understand what smooth manifolds admit a symplectic struct...

Rational tree relations

We investigate forests and relations on trees generated by grammars in which the non-terminals represent relations. This introduces some synchronization between productions. We show that these sets are also solutions of systems of equations, that they are described by rational expressions involving union, substitution and iterated substitution, and that they are preserved by residuals. We show ...

Uniformization of Rational Relations

Rational relations having a rational trace on each finite intersection of rational relations

We consider the family of rational relations on words, i.e., relations recognized by multitape automata, which have rational trace on any finite intersection of rational relations. We prove that this family consists of finite unions of relations which are of two types: stars of tuples possibly with an extra prefix and suffix and relations with all but one singleton set components.