The intersection graph of an orientable generic surface

Ben Hadar, Doron

doi:10.2140/agt.2017.17.1675

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The intersection graph of an orientable generic surface

Doron Ben Hadar

Algebraic & Geometric Topology 17 (2017) 1675–1700

DOI: 10.2140/agt.2017.17.1675

Abstract

The intersection graph $M (i)$ of a generic surface $i : F \to S^{3}$ is the set of values which are either singularities or intersections. It is a multigraph whose edges are transverse intersections of two surfaces and whose vertices are triple intersections and branch values. $M (i)$ has an enhanced graph structure which Gui-Song Li referred to as a “daisy graph”. If $F$ is oriented, then the orientation further refines the structure of $M (i)$ into what Li called an “arrowed daisy graph”.

Li left open the question “which arrowed daisy graphs can be realized as the intersection graph of an oriented generic surface?” The main theorem of this article will answer this. I will also provide some generalizations and extensions to this theorem in Sections 4 and 5.

Keywords

generic surfaces, immersed surfaces in 3-manifolds, intersection graph

Mathematical Subject Classification 2010

Primary: 57N10, 57N12

Secondary: 57N35, 57N40, 57N75

References

Publication

Received: 20 January 2016

Accepted: 2 July 2016

Published: 17 July 2017

Authors

Doron Ben Hadar
Department of Mathematics Bar-Ilan University 5290002 Ramat Gan Israel
http://math.biu.ac.il/node/641

Volume 17, issue 3 (2017)