Spinal open books and algebraic torsion in contact 3-manifolds

By the Giroux correspondence, contact structures on a closed manifold
can be understood in terms of open book decompositions that support
them. A "spinal" open book is a more general notion that also supports
contact structures, and arises naturally e.g. on the boundary of a
Lefschetz fibration whose fibers and base are both oriented surfaces
with boundary.  One can learn much about symplectic fillings by
studying spinal open books: for instance, using holomorphic curve
methods, we can classify the Stein fillings of S^1-invariant contact
structures on circle bundles over oriented surfaces (joint work with
Sam Lisi and Jeremy Van Horn-Morris).  One can also use them to
construct symplectic cobordisms via a natural operation known as
"spine removal surgery", or to compute an invariant that lives in
Symplectic Field Theory and measures the "degree of tightness" of a
contact 3-manifold (joint work with Janko Latschev)