books

Geometric Group Theory. An Introduction.
(
draft pdf
).
Universitext,
Springer,
ISBN 9783319722535,
01/2018.
Errata:
pdf

Quod erat knobelandum,
Themen, Aufgaben und Lösungen des Schülerzirkels Mathematik der Universität Regensburg.
Editors: Clara Löh,
Stefan Krauss,
Niki Kilbertus
Authours:
Andreas Eberl, Alexander Engel, Timo Keller, Niki Kilbertus, Stefan Krauss, Clara Löh, Christian Nerf, Theresa Stoiber, JanHendrik Treude, Alexander Voitovitch
Springer Spektrum,
ISBN 9783662489550, 04/2016.
journal publications

Exotic finite functorial seminorms on singular homology
( pdf ).
Joint work with
Daniel Fauser
Also available at the arXiv:
1605.04093 [math.GT]
Original publication in
Glasgow Mathematical Journal:
The DOI is
DOI 10.1017/S0017089518000216

Odd manifolds of small integral simplicial volume
( pdf ).
Also available at the arXiv:
1509.00204 [math.GT]
Original publication in
Arkiv för Matematik
:
Arkiv för Matematik, volume 56(2), pp. 351375, 2018.
The DOI is
DOI 10.4310/ARKIV.2018.v56.n2.a10

Rank gradient vs. stable integral simplicial volume
( pdf ).
Also available at the arXiv:
1704.05222 [math.GT]
Original publication in
Periodica Mathematica Hungarica:
The DOI is
DOI 10.1007/s1099801702121,
Period Math Hung, volume 76(1), pp. 8894, 2018.
Fulltext viewonly pdf:
pdf

The l^inftyseminorm on uniformly finite homology
( pdf ).
Joint work with
Francesca Diana
Version with longer appendix:
pdf
Also available at the arXiv:
1502.01177 [math.MG]
Original publication in
Forum Mathematicum:
Forum Math., volume 29(6), pp. 13251336, 2017.
The DOI is 10.1515/forum20150258.

Integral foliated simplicial volume of aspherical manifolds
( pdf ).
Joint work with
Roberto Frigerio,
Cristina Pagliantini,
Roman Sauer
Also available at the arXiv:
1506.05567 [math.GT]
Original publication in
Israel Journal of Mathematics:
(link to pdf,
public access viewonly pdf).
Israel J. Math., volume 216(2), pp. 707751, 2016.

On stability of nondomination under taking products
( pdf ).
Joint work with
D. Kotschick,
Christoforos Neofytidis
Also available at the arXiv:
1507.01413 [math.GT]
Published by
Proceedings of the AMS,
Volume 144, pp. 27052710, 2016.
The DOI is 10.10960/proc/13043

A note on boundedcohomological dimension of discrete groups
( pdf ).
Also available at the arXiv:
1504.05760 [math.GR]
Published by
Journal of the Mathematical Society of Japan, Volume 69(2), pp. 715734, 2017.

Finite functorial seminorms and representability
( pdf ).
Also available at the arXiv:
1404.6557 [math.AT]
Published by
International Mathematics Research Notices, Volume 2016(12),
pp. 36163638, 2016.
The DOI is 10.1093/imrn/rnv250.
(pdf)

Integral foliated simplicial volume of hyperbolic 3manifolds
( pdf ).
Joint work with
Cristina Pagliantini
Also available at the arXiv:
1403.4518 [math.GT]
Original publication in
Groups, Geometry, and Dynamics
:
(link to pdf).
Groups Geom. Dyn., volume 10(3), pp. 825865, 2016.

Functorial seminorms on singular homology and (in)flexible manifolds
( pdf ).
Joint work with
Diarmuid Crowley
Also available at the arXiv:
1103.4139 [math.GT]
Published by
Algebraic & Geometric Topology
, Volume 15(3),
pp. 14531499, 2015.
The DOI is 10.2140/agt.2015.15.1453.

Which finitely generated Abelian groups admit isomorphic Cayley graphs?
( pdf ).
Also available at the arXiv:
1202.5484 [math.GR]
Published by
Geometriae Dedicata, Volume 164, pp. 97111, 2013.
The original publication is available at
www.springerlink.com.
The DOI is 10.1007/s107110129761x.

Groups not presentable by products
( pdf ).
Joint work with
D. Kotschick
Also available at the arXiv:
1003.3853 [math.GR]
First published in
Groups, Geometry, and Dynamics
( pdf ),
Volume 7(1), pp. 181204, 2013.

Simplicial volume of Hilbert modular varieties
( pdf ).
Joint work with
Roman Sauer.
Also available at the
arXiv:
0706.3904.
Published by Commentarii Mathematici Helvetici
( pdf ),
Comment. Math. Helv., Volume 84, pp. 457470, 2009.

Degree theorems and Lipschitz simplicial volume for nonpositively
curved manifolds of finite volume
( pdf ).
Joint work with
Roman Sauer.
Also available at the
arXiv:
0710.1635.
Published by the Journal of Topology
( pdf ),
Journal of Topology, Volume 2, pp. 193225, 2009.
Also available through the
Journal of Topology Virtual Issue

Fundamental classes not representable by products
( pdf
).
Joint work with
D. Kotschick
Also available at the
arXiv:
0806.4540 [math.GT].
Published by the Journal of the London Mathematical Society
( pdf
),
J. London Math. Soc. Volume 79, Number 3, pp. 545561 2009.

Isomorphisms in l^1homology
( pdf, previous version ).
Also available at the
arXiv:
math.AT/0612589.
Münster Journal of
Mathematics
( pdf ),
Volume 1, pp. 237266, 2008.

Measure homology and singular homology are isometrically isomorphic
(pdf
).
Also available at the
arXiv:
math.AT/0504103
Published by Mathematische Zeitschrift. The original publication is
available at
www.springerlink.com.
The DOI is 10.1007/s0020900509057. The complete reference of the
printed version is:
Mathematische Zeitschrift, Volume 253, Number 1, pp. 197218, 2006.
preprints
other contributions/notes
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.