2022 Volume 74 Issue 3 Pages 683-717
We prove that the (𝜏-weighted, sheaf-theoretic) SL(2,ℂ) Casson–Lin invariant introduced by Manolescu and the first author is generically independent of the parameter 𝜏 and additive under connected sums of knots in integral homology 3-spheres. This addresses two questions asked by Manolescu and the first author. Our arguments involve a mix of topology and algebraic geometry, and rely crucially on the fact that the SL(2,ℂ) Casson–Lin invariant admits an alternative interpretation via the theory of Behrend functions.
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