Geodesic
The intersection graph of an orientable generic surface
Ben Hadar, Doron1
1Department of Mathematics, Bar-Ilan University, 5290002 Ramat Gan, Israel
Algebraic and Geometric Topology, Tome 17 (2017) no. 3, pp. 1675-1700
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The intersection graph M(i) of a generic surface i: F → S3 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.

DOI : 10.2140/agt.2017.17.1675
Classification : 57N10, 57N12, 57N35, 57N40, 57N75
Keywords: generic surfaces, immersed surfaces in 3-manifolds, intersection graph

Ben Hadar, Doron  1

1 Department of Mathematics, Bar-Ilan University, 5290002 Ramat Gan, Israel 
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Ben Hadar, Doron. The intersection graph of an orientable generic surface. Algebraic and Geometric Topology, Tome 17 (2017) no. 3, pp. 1675-1700. doi: 10.2140/agt.2017.17.1675

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