Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moment maps, symplectomorphism groups and compatible complex structures   In this paper we apply Donaldson's general moment map framework for the
action of a symplectomorphism group on the corresponding space of compatible
(almost) complex structures to the case of rational ruled surfaces. This gives
a new approach to understanding the topology of their symplectomorphism groups,
based on a result of independent interest: the space of compatible integrable
complex structures on any symplectic rational ruled surface is (weakly)
contractible. We also explain how in general, under this condition, there is a
direct relationship between the topology of a symplectomorphism group, the
deformation theory of compatible complex structures and the groups of complex
automorphisms of these complex structures.

23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat