Verschlingungsinvarianten und Bandflächen eingebetteter Graphen

Abstract

In classical knot-theory the linking-number of a link can be calculated from the crossingsof a diagram. This method can be extended to diagrams of spatial graphs. For any abstractgraph this leads to a set of linking-invariants with a structure of a free Z module. It isshown that this module is isomorphic to the linking-module defined by K. Taniyama. Afterthat a basis of the linking-module for the 3-connected simple graphs is constructed. Theelements of that basis are derived from certain subgraphs homeomorphic to K3;3, K5 or disjoint circles . As an application, linking-modules of M¨obius ladders can be calculatedin that way. These elements are used to define unique disk/band surfaces for spatial M¨obiusladders in 3-space with the help of the Gordon-Litherland-form. Up to now constructionsof unique disk/band-surfaces are known only for special classes of planar graphs.