  In the bottom-up approach of emergent gravity we attempt to find symplectic
gauge fields emerging from Euclidean Schwarzschild instanton, which is studied
as electromagnetism defined on the symplectic space $(M,\omega)$. Geometrical
engineering with the emergent metric sets up the Seiberg Witten map between
commutative and non-commutative gauge fields, preparing the ground for the
evaluation of topological invariants in terms of the underlying gauge theory
quantities.
