On Sullivan's theorem of the normal invariant of homeomorphism.
Yuli B. Rudyak
In his paper about Hauptvermutung for manifolds (1967) Sullivan indicated the proof of the following theorem:
Let h: M-->N be a homeomorphism of closed piecewise linear manifolds. Then the normal invariant of h is trivial provided 3-dimensional homology of M has no 2-torsion.
The goal of this paper is to give a relative simple proof of this theorem in a particular case of manifolds M such that the fundamental and homology group of M are free abelian groups. Motivation: Kirby--Siebenmann proved that TOP/PL is the Eilenberg--Mac Lane space K(Z/2,3) and it actually solves the Hauptvermutung for manifolds. The proof by Kirby--Siebenmann uses a special case of the Normal Invariant Homeomorphism Theorem when M is the product of a torus with a sphere.