Additivity of the support norm for tight contact structures
 
A corollary of Haken's Theorem gives that the minimal genus of Heegaard
splittings of 3-manifolds is additive under connected sum. In this talk I
generalise this result for contact 3-manifolds. There is an adapted version of
Heegaard splittings for contact 3-manifolds, that splits up a contact
3-manifold into two tight handlebodies with a prescribed contact structure
near their boundaries.  
These contact Heegaard splitting are in one-to-one correspondence with open
book decompositions. There is a simple homological counterexample of Ozbagci,
showing that the minimal genus for these contact Heegaard splittings is not
additive in general. After introducing the basic notions, I describe the main
idea of the proof, that the minimal genus for contact Heegaard splittings of
tight contact structures is additive under connected sum.