Séminaire de Géométrie Tropicale

Institut Mathématiques de Jussieu ,
Université Pierre et Marie Curie, Paris 6
UMR CNRS 7586




26 septembre 2012, 16h15 salle 1525-502



Selman Akbulut (Michigan State University)

Résumé : Ropes
Taking big chunks out of smooth 4-manifolds and re-glueing them back can result change the smooth structures. A. Akhmedov and B. D. Park used this kind of operation to construct very small exotic compact manifolds without boundary. While showing these operations give exotic manifolds is not that hard, understanding their topology proved to be very difficult. Breaking these chunks into understandable small corks is still an open problem (although theoretically it is possible). One way to perform this operation on a handlebody is by what we call the "roping'' technique. It is performed by exaggerating the gluing region by extreme pulling, and turning them into ropes. You might think of this as smooth "tropicalization" process.