Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructions of small symplectic 4-manifolds using Luttinger surgery   In this article we use the technique of Luttinger surgery to produce small
examples of simply connected and non-simply connected minimal symplectic
4-manifolds. In particular, we construct: (1) An example of a minimal
symplectic 4-manifold that is homeomorphic but not diffeomorphic to
CP^2#3(-CP^2) which contains a symplectic surface of genus 2, trivial normal
bundle, and simply connected complement and a disjoint nullhomologous
Lagrangian torus with the fundamental group of the complement generated by one
of the loops on the torus. (2) A minimal symplectic 4-manifold that is
homeomorphic but not diffeomorphic to 3CP^2#5(-CP^2) which has two essential
Lagrangian tori with simply connected complement. These manifolds can be used
to replace E(1) in many known theorems and constructions. Examples in this
article include the smallest known minimal symplectic manifolds with abelian
fundamental groups including symplectic manifolds with finite and infinite
cyclic fundamental group and Euler characteristic 6.

37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin