Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic mapping class groups of some Stein and rational surfaces   In this paper we compute the homotopy groups of the symplectomorphism groups
of the 3-, 4- and 5-point blow-ups of the projective plane (considered as
monotone symplectic Del Pezzo surfaces). Along the way, we need to compute the
homotopy groups of the compactly supported symplectomorphism groups of the
cotangent bundle of $\mathbf{RP}^{2}$ and of $\mathbf{C}^*\times\mathbf{C}$. We
also make progress in the case of the $A_n$-Milnor fibres: here we can show
that the (compactly supported) Hamiltonian group is contractible and that the
symplectic mapping class group embeds in the braid group on $n$-strands.

8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci