Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Circle actions on almost complex manifolds with 4 fixed points   Let the circle act on a compact almost complex manifold $M$. In this paper,
we classify the fixed point data of the action if there are 4 fixed points and
the dimension of the manifold is at most 6. First, if $\dim M=2$, then $M$ is a
disjoint union of rotations on two 2-spheres. Second, if $\dim M=4$, we prove
that the action alikes a circle action on a Hirzebruch surface. Finally, if
$\dim M=6$, we prove that six types occur for the fixed point data;
$\mathbb{CP}^3$ type, complex quadric in $\mathbb{CP}^4$ type, Fano 3-fold
type, $S^6 \cup S^6$ type, and two unknown types that might possibly be
realized as blow ups of a manifold like $S^6$. When $\dim M=6$, we recover the
result by Ahara in which the fixed point data is determined if furthermore
$\mathrm{Todd}(M)=1$ and $c_1^3(M)[M] \neq 0$, and the result by Tolman in
which the fixed point data is determined if furthermore the base manifold
admits a symplectic structure and the action is Hamiltonian.

16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin