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The signature of a splice

Abstract

We study the behavior of the signature of colored links [Flo05, CF08] under the splice operation. We extend the construction to colored links in integral homology spheres and show that the signature is almost additive, with a correction term independent of the links. We interpret this correction term as the signature of a generalized Hopf link and give a simple closed formula to compute it.Comment: Updated version. Sign corrected in Theorems 2.2 and 2.10 of the previous version. Also Corollary 2.6 was corrected and an Example added. 24 pages, 5 figures. To appear in IMR

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