Families of contact 3-manifolds with arbitrarily large Stein fillings

R. Inanç Baykur, Jeremy Van Horn-Morris, Samuel Lisi, Chris Wendl
2015 Journal of differential geometry  
We show that there are vast families of contact 3-manifolds each member of which admits infinitely many Stein fillings with arbitrarily big euler characteristics and arbitrarily small signatures -which disproves a conjecture of Stipsicz and Ozbagci. To produce our examples, we set a framework which generalizes the construction of Stein structures on allowable Lefschetz fibrations over the 2-disk to those over any orientable base surface, along with the construction of contact structures via
more » ... structures via open books on 3-manifolds to spinal open books introduced in [24].
doi:10.4310/jdg/1445518920 fatcat:2bfggsn3fndbphtcv7ipzs3sea