Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Geometry of the Master Equation and Topological Quantum Field Theory   In Batalin-Vilkovisky formalism a classical mechanical system is specified by
means of a solution to the {\sl classical master equation}. Geometrically such
a solution can be considered as a $QP$-manifold, i.e. a super\m equipped with
an odd vector field $Q$ obeying $\{Q,Q\}=0$ and with $Q$-invariant odd
symplectic structure. We study geometry of $QP$-manifolds. In particular, we
describe some construction of $QP$-manifolds and prove a classification theorem
(under certain conditions).
  We apply these geometric constructions to obtain in natural way the action
functionals of two-dimensional topological sigma-models and to show that the
Chern-Simons theory in BV-formalism arises as a sigma-model with target space
$\Pi {\cal G}$. (Here ${\cal G}$ stands for a Lie algebra and $\Pi$ denotes
parity inversion.)

29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int