Helge Moeller Pedersen

Title: Splice Diagrams and Universal Abelian Covers.

Abstract: A 3-dimensional graph manifold, i.e. a manifold with only
Seifert fibered pieces in its JSJ-decomposition, has many graph
invariants. This talk will be about the one called splice
diagram. Splice diagrams were originally defined for integer homology
spheres, but were recently generalized to all rational homology
spheres. I will talk about several properties of the manifold that
can be seen from the splice diagram, most importantly that if two
manifolds have the same splice diagram, then their universal abelian
covers are homeomorphic.