Abstracts for Oberseminar Differentialgeometrie

This is joint work with Hansjörg Geiges. Extending our work on Cerf's theorem we apply our moduli-theoretic version of Eliashberg-Hofer's filling-with-holomorphic-discs method to symplectic manifolds with cylindrical ends. Is the tight 3-sphere one of its positive ends we obtain existence results for contractible closed Reeb orbits, filling obstructions, and non-existence results for Liouville cobordisms.

Teichmuller spaces for surfaces of infinite type can be studied with geometric techniques, like the pair of pants decomposition and and Fenchel-Nielsen coordinates. In this case we have countably infinitely many pairs-of-pants and coordinates. With these techniques we can describe, under certain hypotheses, the topology given by the Teichmuller distance and the topology given by the "length spectrum" distance.