Spanning solids and Murasugi sum in dimension four
Geometric Topology
2026-07-10 v1
Abstract
We study various constructions of spanning solids for knotted surfaces in the 4-sphere. In particular, we consider a 4-dimensional analogue of Murasugi sum, which we use to define a notion of arborescent knotted surfaces. We give a variety of examples and applications to broken surface diagrams, such as deciding which resolutions of the crossings in these diagrams yield spanning solids.
Cite
@article{arxiv.2607.10018,
title = {Spanning solids and Murasugi sum in dimension four},
author = {Homayun Karimi and Seungwon Kim and Thomas Kindred and Maggie Miller and Patrick Naylor},
journal= {arXiv preprint arXiv:2607.10018},
year = {2026}
}
Comments
60 pages+references, 63 figures