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arXiv · 1801.06585

On two types of $Z$-monodromy in triangulations of surfaces

Mark Pankov·Adam Tyc
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Abstract

Let $Γ$ be a triangulation of a connected closed $2$-dimensional (not necessarily orientable) surface. Using zigzags (closed left-right paths), 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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Mark Pankov, Adam Tyc. 2018-11-04. On two types of $Z$-monodromy in triangulations of surfaces. https://arxiv.org/abs/1801.06585

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