Knotted surfaces and equivalencies of their diagrams without triple points

Details Knotted surfaces and equivalencies of their diagrams without triple points Knotted surfaces and equivalencies of their diagrams without triple points

2010-11-29

arxiv.org/abs/1011.6112v1

Mathematics

Geometric Topology

Scientific paper

10.1142/S0218216511009790

The singularity set of a generic standard projection to the three space of a closed surface linked in four space, consists of at most three types: double points, triple points or branch points. We say that this generic projection image is p-diagram if it does not contain any triple point. Two p-diagrams of equivalent surface links are called p-equivalent if there exists a finite sequence of local moves, such that each of them is one of the four moves taken from the seven on the well known Roseman list, that connects only p-diagrams. It is natural to ask: are any of two p-diagrams of equivalent surface links always p-equivalent? We introduce an invariant of p-equivalent diagrams and an example of linked surfaces that answers our question negatively.

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