Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/30755
Title: Connectivity results for surface branched ideal triangulations
Authors: Benedetti, Riccardo
Keywords: triangulation of surfacesbranchingbranched flips
Issue Date: 2020
Publisher: EUT Edizioni Università di Trieste
Source: Riccardo Benedetti, "Connectivity results for surface branched ideal triangulations" in: "Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 52 (2020)", EUT Edizioni Università di Trieste, Trieste, 2020
Journal: Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics 
Abstract: 
We consider triangulations of closed surfaces S with a given set of vertices V ; every triangulation can be branched that is enhanced to be a Δ-complex. Branched triangulations are considered up to the b-transit equivalence generated by b-flips (i.e. branched diagonal exchanges) and isotopy keeping V pointwise fixed. We extend a well-known connectivity result for 'naked' triangulations; in particular, in the generic case when χ(S) < 0, we show that each branched triangulation is connected to any other if χ(S) is even, while this holds also for odd χ(S) possibly after the complete inversion of one of the two branchings. Natural distribution of the b-flips in sub-families gives rise to restricted transit equivalences with nontrivial (even infinite) quotient sets. We analyze them in terms of certain structures of geometric/topological nature carried by each branched triangulation, invariant for the given restricted equivalence.
Type: Article
URI: http://hdl.handle.net/10077/30755
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/30755
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.52 (2020), 1st and 2nd Issue

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