Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Grafting, pruning, and the antipodal map on measured laminations   Grafting a measured lamination on a hyperbolic surface defines a self-map of
Teichmuller space, which is a homeomorphism by a result of Scannell and Wolf.
In this paper we study the large-scale behavior of pruning, which is the
inverse of grafting.
  Specifically, for each conformal structure $X \in \T(S)$, pruning $X$ gives a
map $\ML(S) \to \T(S)$. We show that this map extends to the Thurston
compactification of $\T(S)$, and that its boundary values are the natural
antipodal involution relative to $X$ on the space of projective measured
laminations.
  We use this result to study Thurston's grafting coordinates on the space of
$\CP^1$ structures on $S$. For each $X \in \T(S)$, we show that the boundary of
the space $P(X)$ of $\CP^1$ structures on $X$ in the compactification of the
grafting coordinates is the graph $\Gamma(i_X)$ of the antipodal involution
$i_X : \PML(S) \to \PML(S)$.

17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs