Séminaire de Géométrie Tropicale
26 septembre 2012, 16h15 salle 1525-502
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.