doctoral thesis: l^1Homology and Simplicial Volume
I wrote my
doctoral thesis
under supervision of
Prof. Dr. W. Lück.
Abstract.
Taking the l^1completion and the topological dual of the singular chain complex
gives rise to l^1homology and bounded cohomology respectively. Unlike l^1homology,
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^1homology.
For example, we obtain a new, simple proof of the fact that l^1homology depends only
on the fundamental group and that l^1homology with twisted coefficients admits a
description in terms of projective resolutions. In the second part, we study applications
of l^1homology concerning the simplicial volume of noncompact manifolds.
Stable URL:
http://nbnresolving.de/urn:nbn:de:hbz:637549578216
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 CWcomplexes.
