Abstract
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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
