English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider triangulations of closed surfaces S with a given set of verticesV; every triangulation can be branched that is enhanced to a Delta-complex.Branched triangulations are considered up to the b-transit equivalencegenerated by b-flips (i.e. branched diagonal exchanges) and isotopy keeping Vpoint-wise fixed. We extend a well known connectivity result for `naked'triangulations; in particular in the generic case when S has negativeEuler-Poincare' characteristic c(S), we show that branched triangulations areequivalent to each other if c(S) is even, while this holds also for odd c(S)possibly after the complete inversion of one of the two branchings. Moreover weshow that under a mild assumption, two branchings on a same triangulation areconnected via a sequence of inversions of ambiguous edges (and possibly thetotal inversion of one of them). A natural organization of the b-flips insubfamilies gives rise to restricted transit equivalences with non trivial(even infinite) quotient sets. We analyze them in terms of certain preservedstructures of differential topological nature carried by any branchedtriangulations; in particular a pair of transverse foliations with determinedsingular sets contained in V, including as particular cases the configurationof the vertical and horizontal foliations of the square of an Abeliandifferential on a Riemann surface.

On ideal triangulations of surfaces up to branched transit equivalences