# A note on the nearly additivity of knot width - Mathematics > Geometric Topology

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Abstract: Let k be a knot in S3. In 8, H.N. Howards and J. Schultens introduced amethod to construct a manifold decomposition of double branched cover of S3,k from a thin position of k. In this article, we will prove that if a thinposition of k induces a thin decomposition of double branched cover of S3,kby Howards and Schultens- method, then the thin position is the sum of primesummands by stacking a thin position of one of prime summands of k on top of athin position of another prime summand, and so on. Therefore, k holds thenearly additivity of knot width i.e. for k = k1#k2, wk = wk1#wk2 - 2 inthis case. Moreover, we will generalize the hypothesis to the property a thinposition induces a manifold decomposition whose thick surfaces consists ofstrongly irreducible or critical surfaces so topologically minimal.

Author: ** Jungsoo Kim**

Source: https://arxiv.org/