On two types of Z-monodromy in triangulations of surfaces

Add time:08/21/2019    Source:sciencedirect.com

Let Γ be a triangulation of a connected closed 2-dimensional (not necessarily orientable) surface. Using zigzags (closed left–right walks), for every face of Γ we define the z-monodromy which acts on the oriented edges of this face. There are precisely 7 types of z-monodromies. We consider the following two cases: (M1) the z-monodromy is identity, (M2) the z-monodromy is the consecutive passing of the oriented edges. Our main result is the following: the subgraphs of the dual graph Γ∗ formed by edges whose z-monodromies are of types (M1) and (M2), respectively, both are forests. We apply this statement to the connected sum of z-knotted triangulations.

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