Abstract:
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.
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