  The deformation retract is, by definition, a homotopy between a retraction
and the identity map. We show that applying this topological concept to
Ricci-flat wormholes/black holes implies that such objects can get deformed and
reduced to lower dimensions. The homotopy theory can provide a rigorous proof
to the existence of black holes/wormholes deformations and explain the
topological origin. The current work discusses such possible deformations and
dimensional reductions from a global topological point of view, it also
represents a new application of the homotopy theory and deformation retract in
astrophysics and quantum gravity.
