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Abstract. We construct a combinatorial invariant of 3-orbifolds with singular set a link that generalizes the Turaev torsion invariant of 3-manifolds. We give several gluing formulas from which we derive two consequences. The first is an understanding of how the components of the invariant change when we remove a curve from the singular set. The second is a formula relating the invariant of the 3-orbifold to the Turaev torsion invariant of the underlying 3-manifold in the case when the singular set is a nullhomologous knot.

In [6], Auckly-Kim-Melvin-Ruberman showed that for any finite subgroup G of SO(4) there exists a contractible smooth 4-manifold with an effective G-action on its boundary so that the twists associated to the non-trivial elements of G don't extend to diffeomorphisms of the entire manifold. We give a different proof of this phenomenon using the Heegaard Floer theoretic argument in [3]. arXiv:1609.04857v1 [math.GT]

Using bordered Floer theory, we construct an invariant HFO(Y orb ) for 3orbifolds Y orb with singular set a knot that generalizes the hat flavor HF (Y ) of Heegaard Floer homology for closed 3-manifolds Y . We show that for a large class of 3-orbifolds HFO behaves like HF in that HFO, together with a relative Z 2 -grading, categorifies the order of H orb 1 . When Y orb arises as Dehn surgery on an integer-framed knot in S 3 , we use the {−1, 0, 1}-valued knot invariant ε to determine the relationship between HFO(Y orb ) and HF (Y ) of the 3-manifold Y underlying Y orb .

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