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We consider the link and three-manifold invariants in [DGGPR], which aredefined in terms of certain non-semisimple finite ribbon categories$\mathcal{C}$ together with a choice of tensor ideal and modified trace. If theideal is all of $\mathcal{C}$, these invariants agree with those defined byLyubashenko in the 90's. We show that in that case the invariants depend on theobjects labelling the link only through their simple composition factors, sothat in order to detect non-trivial extensions one needs to pass to properideals. We compute examples of link and three-manifold invariants for$\mathcal{C}$ being the category of $N$ pairs of symplectic fermions. Using aquasi-Hopf algebra realisation of $\mathcal{C}$, we find that theLyubashenko-invariant of a lens space is equal to the order of its firsthomology group to the power $N$, a relation we conjecture to hold for allrational homology spheres. For $N \ge 2$, $\mathcal{C}$ allows for tensorideals $\mathcal{I}$ with a modified trace which are different from all of$\mathcal{C}$ and from the projective ideal. Using the theory of pull-backtraces and symmetrised cointegrals, we show that the link invariant obtainedfrom $\mathcal{I}$ can distinguish a continuum of indecomposable but reducibleobjects which all have the same composition series.

Non-semisimple link and manifold invariants for symplectic fermions