The Atiyah–Patodi–Singer rho invariant and signatures of links

Abstract Relations between the Atiyah–Patodi–Singer rho invariant and signatures of links have been known for a long time, but they were only partially investigated. In order to explore them further, we develop versatile cut-and-paste formula invariant, which allows us manipulate manifolds in convenient way. With help this tool, give description multivariable signature link $L$ as some closed three-manifold $Y_L$ intrinsically associated with . We study then obtained by Dehn surgery on along integer rational framings. Inspired results Casson Gordon Cimasoni Florens, formulas expressing value sum easy-to-compute extra terms.