It is enough to prove the theorem for W since a Reidemeister torsion is a simple homotopy invariant
In thiswork, geometric realization and totalization willmean homotopy invariant
geometric realization and totalization.
Since the Lefschetz number is a homotopy invariant
, it can be used to classify digital images.
However, Aut(X) is not a homotopy invariant
of X, while haut(X) is.
The first k-invariant is a homotopy invariant that belongs to [H.
MacLane Determinationation of the Second Homology and Cohomology Groups ofa Space by Means of Homotopy Invariants.
It is not a numerical but is a graphical (rational) homotopy invariant of spaces.
It must be a topological homotopy invariant of spaces.
The Lusternik-Schnirelmann category, L-S category for short, of a space is a homotopy invariant
defined as follows.
Relative homotopy invariants
of the type of the Lusternik-Schnirelmann category.
Fasso Velenik, Relative homotopy invariants
of the type of the Lusternik-Schnirelmann category, Eingereichte Dissertation (Ph.