The Kakimizu complex of a surface
Open Access Publications from the University of California

## Published Web Location

https://arxiv.org/pdf/1401.2111.pdf
No data is associated with this publication.
Abstract

The Kakimizu complex is usually defined in the context of knots, where it is known to be quasi-Euclidean. We here generalize the definition of the Kakimizu complex to surfaces and 3-manifolds (with or without boundary). Interestingly, in the setting of surfaces, the complexes and the techniques turn out to replicate those used to study the Torelli group, {\it i.e.,} the "nonlinear" subgroup of the mapping class group. Our main results are that the Kakimizu complexes of a surface are contractible and that they need not be quasi-Euclidean. It follows that there exist (product) $3$-manifolds whose Kakimizu complexes are not quasi-Euclidean.

Item not freely available? Link broken?
Report a problem accessing this item