Understanding a curve system on the boundary of Teichmuller space

Question

I am reading the paper:

https://arxiv.org/pdf/1511.07635.pdf

and I try to understand the behavior on the boundary. I have some problems understanding this definition.

On page 26, the authors give a definition of a curve system (Definition 4.6)

Let $\Sigma_{g,n}$ be a Riemann surface of genus $g$ with $n$ marked points $Q=\{q_1,\ldots,q_n\}$. a curve system $c=\{c_i\}_{i\in I}$ in $\Sigma_{g,n}$ is a disjoint collection of simple closed curves $c_i$ on $\Sigma_{g,n}\setminus Q$ such that none of which is isotopic to any other, to a point or to a cylinder in $\Sigma_{g,n}\setminus Q$.

To a curve system $c$ we can associate the subset $B_c\subset T_{g,n}$ of the boundary of the Teichmuller space of stable curves genus $g$ with $n$ marked points consisting of homotopically marked stable curves topologically equivalent to a collapse $\Sigma_g\to \Sigma/c$ obtained by identifying each curve in $c$ to a point.

My questions are:

1. What does a curve isotopic to a cylinder mean?
2. How are the elements of $B_c$?

I will appreciate any comments. Thanks in advance.

Edit

A stable curve $C$ is a complex connected curve with $n$ marked points such that its singularities are nodes and do not coincide with any of the marked points and the closure of each component of $C^*=C\setminus Sing(C)$ has a group of automorphisms that fix the marked points and the boundary points is finite.

Answer 1

I will answer your first question --- and let me also suggest that for a fuller answer you should consult the standard texts on this theory: the books of Farb and Margalit; and of Fathi, Laudenback, Poenaru et. al..

Regarding your question about cylinders, it looks like there is a mistake in the wording: a few words are missing. The correct wording (similar to a later usage of the term cylinder in the paper) should be:

... none of which is isotopic to any other, to a point, or to a curve in a cylinder representing one of the ends of $\Sigma_{g,n} \setminus Q$.