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We prove that the ($\tau$-weighted, sheaf-theoretic) SL(2,C) Casson-Lininvariant introduced by Manolescu and the first author in [CM19] is genericallyindependent of the parameter $\tau$ and additive under connected sums of knotsin integral homology 3-spheres. This addresses two questions asked in [CM19].Our arguments involve a mix of topology, microlocal analysis and algebraicgeometry, and rely crucially on the fact that the SL(2,C) Casson-Lin invariantadmits an alternative interpretation via the theory of Behrend functions.

On the sheaf-theoretic SL(2,C) Casson-Lin invariant