Splitting numbers and signatures

The splitting number of a link is the minimal number of crossing changes between different components required to convert it into a split link. This invariant was studied by Batson-Seed [1] using Khovanov homology, by Cha-Friedl-Powell [2] using the Alexander polynomial and covering link calculus, and by Borodzik-Gorsky [3] using Heegaard-Floer homology.
In this talk, I will prove a new lower bound on the splitting number in terms of the (multivariable) signature and nullity of [4]. Although very elementary and easy to compute, this bound turns out to be suprisingly efficient. In particular, I will show that it compares very favorably to the methods mentioned above.
The talk is based on the joint work [5] with A. Conway and K. Zaharova. The author is partially supported by Swiss National Science Foundation.
References:

• J. Batson, C. Seed, A link-splitting spectral sequence in Khovanov homology, Duke Math. J., Vol. 164 (2015), no. 5, 801–841.
• J. C. Cha, S. Friedl, M. Powell, Splitting numbers of links, Proc. Edinb. Math. Soc. (2), to appear.
• M. Borodzik, E. Gorsky, Immersed concordances of links and Heegaard Floer homology, preprint.
• D. Cimasoni, V. Florens, Generalized Seifert surfaces and signatures of colored links, Trans. Amer. Math. Soc., Vol. 360 (2008), no. 3, 1223–1264.
• D. Cimasoni, A. Conway, K. Zacharova, Splitting numbers and signatures, Proc. Amer. Math. Soc., to appear.