Marco Golla

These are my papers and preprints:

• (with S. Behrens) Heegaard Floer correction terms, with a twist
  Available on the arXiv: arXiv:1505.07401.
  We use Heegaard Floer homology with twisted coefficients to define numerical invariants for arbitrary closed 3-manifolds equipped torsion spin^c structures, generalising the correction terms (or d-invariants) defined by Ozsváth and Szabó for integer homology 3-spheres and, more generally, for 3-manifolds with standard HF-infinity. Our twisted correction terms share many properties with their untwisted analogues. In particular, they provide restrictions on the topology of 4-manifolds bounding a given 3-manifold.

• (with B. Martelli) Pair of pants decompositions of 4-manifolds
  Available on the arXiv: arXiv:1503.05839.
  We study pair of pants decompositions of 4-manifolds, generalising a construction due to Mikhalkin. We construct some nontrivial examples, and in particular we prove that any finitely presented group is the fundamental group of a closed 4-manifold admitting a pants decomposition.

• (with P. Lisca) On Stein fillings of contact torus bundles
  Available on the arXiv: arXiv:1412.0828.
  We construct tight contact structures on some torus bundles over the circle and we study their Stein fillings, up to diffeomorphism. We classify these fillings, showing that uniqueness holds in some cases; we also provide examples where uniqueness doesn’t hold.

• (with J. Bodnár and D. Celoria) Cuspidal curves and Heegaard Floer homology
  Available on the arXiv: arXiv:1409.3282.
  We give bounds on the gap functions of the singularities of a cuspidal plane curve of arbitrary genus. We apply these inequalities to unicuspidal curves whose singularity has one Puiseux pair: we prove some finiteness results, we construct infinite family of examples, and in some cases we give an almost complete classification.

• Ozsváth–Szabó invariants of contact surgeries, Geom. Topol. 19(1) (2015) 171–235.
  We give the computation of the Ozsváth–Szabó contact invariant for positive contact surgeries in the 3-sphere in terms of the classical invariants of the Legendrian knot, and tau and nu (or tau and epsilon) of the underlying topological type.

• Comparing invariants of Legendrian knots, Quantum Topol. 6(3) (2015) 365–402.
  We give a comparison between the EH contact invariant of Honda, Kazez and Matic and the LOSS^– invariant of Lisca, Ozsváth, Stipsicz and Szabó.