Dimension, the number of coordinates required to specify a point in a given space, is an example of a topological invariant
Such deformation spaces often arise as solutions to basic geometric problems, and their global properties provide powerful topological invariants
, in particular for three- and four-dimensional manifolds.
In mathematical terminology, Hirzebruch's problem was to determine which Chern numbers are topological invariants
of complex-algebraic varieties.
Three of the 20 papers delivered at the June 2006 conference survey algorithms for computing topological invariants
of semi-algebraic sets, problems and methods concerning k-facets and k-sets, and several points of view on pseudo-triangulations.
The topological invariants
of a network are those properties that are not altered by elastic deformations.