German Title: Hirzebruch Homologie

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Abstract

The aim of this thesis is to provide a new natural construction of the Hirzebruch homology functor introduced by Matthias Kreck. The Hirzebruch homology allows to define a characteristic class for manifolds which is a sort of integral L-class. This class is related to the Novikov conjecture and to the general problem of classifying manifolds. Our construction is based on one side on Kreck's theory of stratifolds and on the other side on Markus Banagl's theory of self-dual complexes of sheaves. As a corollary we can show that the Hirzebruch fundamental class of a manifold is a topological invariant and we get therefore a slight generalization of Novikov's famous theorem about the topological invariance of the rational Pontrjagin classes.