Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 2 \pi-grafting and complex projective structures, I   Let $S$ be a closed oriented surface of genus at least two. Gallo, Kapovich,
and Marden asked if 2\pi-graftings produce all projective structures on $S$
with arbitrarily fixed holonomy (Grafting Conjecture). In this paper, we show
that the conjecture holds true "locally" in the space $GL$ of geodesic
laminations on $S$ via a natural projection of projective structures on $S$
into $GL$ in the Thurston coordinates. In the sequel paper, using this local
solution, we prove the conjecture for generic holonomy.

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th