Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitely many non-isotopic real symplectic forms on $S^2 \times S^2$   Let $(S^2,\omega)$ be a symplectic sphere, and let $\tau \colon S^2 \to S^2$
be an anti-symplectic involution of $(S^2,\omega)$. We consider the product
$(S^2,\omega) \times (S^2,\omega)$ endowed with the anti-symplectic involution
$\tau \times \tau$, and study the space of monotone anti-invariant symplectic
forms on this four-manifold. We show that this space is disconnected. In
addition, during the course of the proof, we produce a diffeomorphism of the
grassmannian (2,4) which induces the identity map on all homology and homotopy
groups, but which is not homotopic to the identity.

35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics