Basket, flat plumbing and flat plumbing basket surfaces derived from induced graphs

Details Basket, flat plumbing and flat plumbing basket surfaces derived from induced graphs Basket, flat plumbing and flat plumbing basket surfaces derived from induced graphs

2011-08-06

arxiv.org/abs/1108.1455v1

Mathematics

Geometric Topology

17 pages, 9 figures

Scientific paper

The existence of basket, flat plumbing and flat plumbing basket surfaces of a link was first proven from a braid representative of the link. In the present article, we show the existence of such surfaces from an induced graph of the link. Consequently, we define the basket number, flat plumbing number and flat plumbing basket number of a link. Then we provide several upper bounds for these plumbing numbers and study the relation between these plumbing numbers and the genera of links.

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