The Kakimizu complex of a connected sum of links

Details The Kakimizu complex of a connected sum of links The Kakimizu complex of a connected sum of links

2011-09-05

arxiv.org/abs/1109.0965v1

Mathematics

Geometric Topology

23 pages, 8 figures. This result has been proved independently by Bassem Saad

Scientific paper

We show that $|MS(L_1 # L_2)|=|MS(L_1)|\times|MS(L_2)|\times\mathbb{R}$ when
$L_1$ and $L_2$ are any non-split and non-fibred links. Here $MS(L)$ denotes
the Kakimizu complex of a link $L$, which records the taut Seifert surfaces for
$L$. We also show that the analogous result holds if we study incompressible
Seifert surfaces instead of taut ones.

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