Clara Löh

doctoral thesis: l^1-Homology and Simplicial Volume

I wrote my doctoral thesis under supervision of Prof. Dr. W. Lück.

Abstract. Taking the l^1-completion and the topological dual of the singular chain complex gives rise to l^1-homology and bounded cohomology respectively. Unlike l^1-homology, bounded cohomology is quite well understood by the work of Gromov and Ivanov. We derive a mechanism linking isomorphisms on the level of homology of Banach chain complexes to isomorphisms on the level of cohomology of the dual Banach cochain complexes and vice versa. Therefore, certain results on bounded cohomology can be transferred to l^1-homology. For example, we obtain a new, simple proof of the fact that l^1-homology depends only on the fundamental group and that l^1-homology with twisted coefficients admits a description in terms of projective resolutions. In the second part, we study applications of l^1-homology concerning the simplicial volume of non-compact manifolds.

Stable URL: http://nbn-resolving.de/urn:nbn:de:hbz:6-37549578216

errata

A list of errata and comments to my doctoral thesis can be found here.

diploma thesis: The Proportionality Principle of Simplicial Volume

I wrote my diploma thesis under supervision of Prof. Dr. W. Lück.

Abstract. The aim of this diploma thesis is to give a full proof of the proportionality principle of simplicial volume, including a proof of the fact that (smooth) measure homology and singular homology (with real coefficients) are isometrically isomorphic.

The diploma thesis is also available at the arXiv: math.AT/0504106

errata

The manifold M in Corollary 5.10 has to be closed.

Theorem 2.37 is only valid for connected locally finite CW-complexes.