We consider 3-dimensional pseudo-manifolds M with a given set of marked point V such that M-V is the interior of a compact 3-manifold with boundary. An ideal triangulation T of (M, V ) has V as its set of vertices. A branching (T, b) enhances T to a Delta-complex. Branched triangulations of (M, V ) are considered up to the b-transit equivalence generated by isotopy and ideal branched moves which keep V pointwise fixed. We extend a well known connectivity result for naked triangulations by showing that branched ideal triangulations of (M, V) are equivalent to each other. A pre-branching is a system of transverse orientations at the 2-facets of T verifying a certain global constraint; pre-branchings are considered up to a natural pb-transit equivalence. If M is oriented, every branching b induces a pre-branching w(b) and every b-transit induces a pb-transit. The quotient set of pre-branchings up to transit equivalence is far to be trivial; we get some information about it and we characterize the pre-branchings of type w(b). Pre-branched and branched moves are naturally organized in subfamilies which give rise to restricted transit equivalences. In the branching setting we revisit early results about the sliding transit equivalence and outline a conceptually different approach to the branched connectivity and eventually also to the naked one. The basic idea is to point out some structures of differential topological nature which are carried by every branched ideal triangulation, are preserved by the sliding transits and can be modified by the whole branched transits. The non ambiguous transit equivalence already widely studied on pre-branchings lifts to a specialization of the sliding equivalence on branchings; we point out a few specific insights, again in terms of carried structures preserved by the non ambiguous and which can be modified by the whole sliding transits.

中文翻译：

---

3流形的理想三角剖分直到装饰过境等价物

我们考虑具有一组给定标记点 V 的 3 维伪流形 M，使得 MV 是具有边界的紧凑 3 流形的内部。(M, V ) 的理想三角剖分 T 将 V 作为其顶点集。分支 (T, b) 将 T 增强为 Delta 复合体。(M, V ) 的分支三角剖分被认为是由同位素和理想分支移动生成的 b 传输等价，使 V 点方向固定。我们通过证明 (M, V) 的分支理想三角剖分彼此等效，扩展了裸三角剖分的众所周知的连通性结果。预分支是 T 的 2 个面的横向方向系统，用于验证某个全局约束；预分支被认为达到了自然 pb-transit 等效。如果 M 是有向的，每个分支 b 诱导预分支 w(b) 并且每个 b-transit 诱导 pb-transit。达到传输等效的预分支商集远不是微不足道的。我们得到了一些关于它的信息，我们表征了 w(b) 类型的预分支。预分支和分支移动自然地组织在子族中，从而产生受限的过境等价。在分支设置中，我们重新审视了关于滑动传输等价的早期结果，并概述了一种概念上不同的分支连接方法，最终也是裸连接方法。其基本思想是指出一些具有微分拓扑性质的结构，这些结构由每个分支理想三角剖分携带，由滑动传输保留，并且可以被整个分支传输修改。已经在预分支上广泛研究的非歧义传输等价将分支上的滑动等价专门化；我们指出了一些具体的见解，同样是在非歧义保留的携带结构方面，并且可以通过整个滑动过境进行修改。