The Signature of a Splice

Alex Degtyarev (1) , Vincent Florens (2) , Ana G. Lecuona (3)

1 Department of Mathematics [Ankara]
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
3 I2M - Institut de Mathématiques de Marseille

We consider the signature of a colored link in an integral homology sphere and study its behavior under the splice operation. We 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.

Keywords: COLORED LINKS; INVARIANTS; COBORDISM; SURFACES

Domains: Geometric Topology [math.GT]

Alex Degtyarev, Vincent Florens, Ana G. Lecuona. The Signature of a Splice. International Mathematics Research Notices, 2017, 8, pp.2249 - 2283. ⟨10.1093/imrn/rnw068⟩. ⟨hal-01262764⟩