Editing Triangulation (topology) (section)

=== Reidemeister torsion ===
To disprove the Hauptvermutung it is helpful to use combinatorial invariants which are not topological invariants. A famous example is Reidemeister torsion. It can be assigned to a tuple <math>(K,L)</math> of CW-complexes: If <math>L = \emptyset</math> this characteristic will be a topological invariant but if <math>L \neq \emptyset</math> in general not. An approach to Hauptvermutung was to find homeomorphic spaces with different values of Reidemeister torsion. This invariant was used initially to classify lens-spaces and first counterexamples to the Hauptvermutung were built based on lens-spaces:<ref name=":42"/>