The signature of a splice
arXiv:1409.5873 · doi:10.1093/imrn/rnw068
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.
arXiv commentUpdated 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 IMRN