  The reasons of the crisis in the contemporary (Riemannian) geometry are
discussed. The conventional method of the generalized geometries construction,
based on a use of the topology, leads to a overdetermination of the Riemannian
geometry. In other words, at the Riemannian geometry construction one uses the
needless information (topology), which disagrees with other original axioms.
The crisis manifests in the fact, that the mathematical community cannot see
and does not want to see the overdetermination of the Riemannian geometry. The
most geometers-topologists deny the alternative method of the generalized
geometry construction, which does not uses the topology, because it does not
contain theorems. Most geometers see the geometry presentation as a set of
definitions and theorems. They cannot imagine the geometry presentation without
customary theorems. As a result the most clever topologists, which have
acknowledged the negligible role of the topology in the geometry construction
and inconsistency of the conventional method of the generalized geometry
construction, appear in the difficult situation (conflict with the mathematical
community).
