ids
books
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Exploring Formalisation.
A Primer in Human-Readable Mathematics in Lean 3
with Examples from Simplicial Topology
Homepage of this book project (including Lean src),
Surveys and Tutorials in the Applied Mathematical Sciences
, volume 11,
Springer, 09/2022.
print ISBN 978-3-031-14648-0,
ebook ISBN 978-3-031-14649-7,
DOI 10.1007/978-3-031-14649-7
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Ergodic theoretic methods in group homology. A minicourse
on L^2-Betti numbers in group theory.
( draft pdf
).
SpringerBriefs in Mathematics, Springer,
ISBN 978-3-030-44219-4,
DOI 10.1007/978-3-030-44220-0,
03/2020.
Errata:
pdf
-
Geometric Group Theory. An Introduction.
(
draft pdf
).
Universitext,
Springer,
ISBN 978-3-319-72253-5,
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 of the second edition:
Karin Binder, Georg Bruckmaier, Andreas Eberl, Alexander Engel, Gerrit, Herrmann, Timo Keller, Niki Kilbertus, Stefan Krauss, Clara Löh, Christian Nerf, Theresa Stoiber, Jan-Hendrik Treude, Alexander Voitovitch
Springer Spektrum,
ISBN 978-3-662-58724-9, 03/2019.
Authours of the first edition:
Andreas Eberl, Alexander Engel, Timo Keller, Niki Kilbertus, Stefan Krauss, Clara Löh, Christian Nerf, Theresa Stoiber, Jan-Hendrik Treude, Alexander Voitovitch
Springer Spektrum,
ISBN 978-3-662-48955-0, 04/2016.
journal publications
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L^2-Betti numbers and computability of reals
( pdf ).
Joint work with
Matthias Uschold
(Partial) implementation in Lean
Also available at the arXiv:
2202.03159 [math.GR]
To appear in
Computability:
The DOI is
10.3233/COM-220416.
-
The spectrum of simplicial volume with fixed fundamental group
( pdf ).
Also available at the arXiv:
2205.14877 [math.GT]
Original publication in
Geometriae Dedicata:
Geom Dedicata 217, article 16, 2023.
The DOI is
10.1007/s10711-022-00749-9.
Published pdf:
pdf
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Bounded cohomology of finitely presented groups: vanishing, non-vanishing, and computability
( pdf ).
Joint work with
Francesco Fournier Facio,
Marco Moraschini.
Also available at the arXiv:
2106.13567 [math.GR]
To appear in
Annali della Scuola Normale Superiore di Pisa
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On the simplicial volume and the Euler characteristic of (aspherical) manifolds
( pdf ).
Joint work with
Marco Moraschini,
George Raptis.
Also available at the arXiv:
2109.08115 [math.AT]
Original publication in
Research in the Mathematical Sciences: Res Math Sci, 9, article 44, 2022.
The DOI is
10.1007/s40687-022-00341-3.
Published pdf: pdf
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Amenable covers and integral foliated simplicial volume
( pdf ).
Joint work with
Marco Moraschini,
Roman Sauer.
Also available at the arXiv:
2112.12223 [math.GT]
Original publication in
New York Journal of Mathematics:
New York J. Math., 28, pp. 1112--1136, 2022.
Published pdf:
pdf
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Bounded cohomology and binate groups
( pdf ).
Joint work with
Francesco Fournier Facio,
Marco Moraschini.
Also available at the arXiv:
2111.04305 [math.GR]
Original publication in
Journal of the Australian Mathematical Society.
The DOI is
10.1017/S1446788722000106.
Published pdf:
pdf
-
Topological volumes of fibrations: A note on open covers
( pdf ).
Joint work with
Marco Moraschini.
Also available at the arXiv:
2104.06038 [math.GT]
Original publication in
Proceedings A of the Royal Society of Edinburgh
:
Proc. Roy. Soc. Edinburgh Sect. A, 152, pp. 1340--1360, 2022.
The DOI is
10.1017/prm.2021.64
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The spectrum of simplicial volume of non-compact manifolds
( pdf ).
Joint work with
Nicolaus Heuer
Also available at the arXiv:
2010.12945 [math.GT]
Original publication in
Geometriae Dedicata:
Geom. Dedicata, 215, pp. 243--253, 2021.
The DOI is
10.1007/s10711-021-00647-6
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Simplicial volume of one-relator groups and stable commutator length
( pdf ).
Joint work with
Nicolaus Heuer
Implementation of lallop in MATLAB
Implementation of lallop in Haskell
Also available at the arXiv:
1911.02470 [math.GT]
Original publication in Algebraic and Geometric Topology:
Alg. Geom. Top., 22(4), pp. 1615--1661, 2022.
The DOI is 10.2140/agt.2022.22.1615.
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Stable integral simplicial volume of 3-manifolds
( pdf ).
Joint work with
Daniel Fauser,
Marco Moraschini,
José Pedro Quintanilha
Also available at the arXiv:
1910.06120 [math.GT]
Original publication in Journal of Topology: J. Topol., 14(2), pp. 608--640, 2021.
The DOI is 10.1112/topo.12193.
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Epimorphism testing with virtually Abelian targets
( pdf ).
Joint work with
Stefan Friedl
Also available at the arXiv:
2010.07537 [math.GR]
Original publication in Confluentes Mathematici:
Confluentes Math., 13(1), pp. 61--78, 2021.
published pdf
-
Amenable category and complexity
( pdf ).
Joint work with
Pietro Capovilla
and
Marco Moraschini
Also available at the arXiv:
2012.00612 [math.AT]
Original publication in Algebraic and Geometric Topology:
Alg. Geom. Topol., 22(3), pp. 1417--1459, 2022.
The DOI is 10.2140/agt.2022.22.1417.
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Transcendental simplicial volumes
( pdf ).
Joint work with
Nicolaus Heuer
Also available at the arXiv:
1911.06386 [math.GT]
To appear in Annales de l'Institut Fourier
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The spectrum of simplicial volume
( pdf ).
Joint work with
Nicolaus Heuer
Also available at the arXiv:
1904.04539 [math.GT]
Original publication in Inventiones mathematicae:
Invent. math., 223, pp. 103--148, 2021.
The DOI is
10.1007/s00222-020-00989-0
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A note on p-adic simplicial volumes
( pdf ).
Joint work with
Steffen Kionke
Also available at the arXiv:
2003.10756 [math.GT]
Original publication in
Glasgow Mathematical Journal:
Glasgow Math. J., 63(3), pp. 563--583, 2021.
The DOI is
10.1017/S0017089520000385
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Bounded cohomology of amenable covers via classifying spaces
( pdf ).
Joint work with
Roman Sauer
Also available at the arXiv:
1910.11716 [math.AT]
Original publication in L'Enseignement Mathématique:
Enseign. Math., 66(1/2), pp. 151--172, 2020.
The DOI is
10.4171/LEM/66-1/2-8
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Simplicial volume via normalised cycles
( pdf ).
Joint work with
Marco Moraschini
Also available at the arXiv:
2003.02584 [math.AT]
Original publication in
Proceedings of the AMS:
Proc. Amer. Math. Soc., 148(12), pages 5437--5440, 2020.
The DOI is
10.1090/proc/15201
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Polynomially weighted l^p-completions and group homology
( pdf ).
Joint work with
Alexander Engel
Also available at the arXiv:
1903.11486 [math.GR]
Original publication in
Journal of Combinatorial Algebra:
J. Comb. Algebra, volume 4(1), pp. 87--109, 2020.
The DOI is 10.4171/JCA/40
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Cost vs. integral foliated simplicial volume
( pdf ).
Also available at the arXiv:
1809.09660 [math.GT]
Original publication in
Groups, Geometry, and Dynamics:
Groups Geom. Dyn., 14(3), pp. 899--916, 2020.
The DOI is
10.4171/GGD/568
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Simplicial volume with F_p-coefficients
( pdf ).
Also available at the arXiv:
1808.09497 [math.GT]
Original publication in
Periodica Mathematica Hungarica:
Period Math Hung, volume 80(1), pp. 38--58, 2020.
The DOI is
DOI 10.1007/s10998-019-00298-x
Full-text pdf:
pdf
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Integral approximation of simplicial volume of graph manifolds
( pdf ).
Joint work with
Daniel Fauser
and
Stefan Friedl
Also available at the arXiv:
1807.10522 [math.GT]
Original publication in
Bulletin of the London Mathematical Society:
Bull. Lond. Math. Soc., 51(4), pp. 715--731, 2019.
The DOI is
DOI 10.1112/blms.12266
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Variations on the theme of the uniform boundary condition
( pdf ).
Joint work with
Daniel Fauser
Also available at the arXiv:
1703.01108 [math.GT]
Original publication in
Journal of Topology and Analysis:
J. Topol. Anal., 13(1), pp. 147--174, 2021.
The DOI is
DOI 10.1142/S1793525320500090
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Exotic finite functorial semi-norms on singular homology
( pdf ).
Joint work with
Daniel Fauser
Also available at the arXiv:
1605.04093 [math.GT]
Original publication in
Glasgow Mathematical Journal:
Glasgow Mathematical Journal, volume 61(2), pp. 287--295, 2019.
The DOI is
DOI 10.1017/S0017089518000216
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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. 351--375, 2018.
The DOI is
DOI 10.4310/ARKIV.2018.v56.n2.a10
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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/s10998-017-0212-1,
Period Math Hung, volume 76(1), pp. 88--94, 2018.
Full-text view-only pdf:
pdf
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The l^infty-semi-norm 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. 1325--1336, 2017.
The DOI is 10.1515/forum-2015-0258.
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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 view-only pdf).
Israel J. Math., volume 216(2), pp. 707--751, 2016.
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On stability of non-domination 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. 2705--2710, 2016.
The DOI is 10.10960/proc/13043
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A note on bounded-cohomological 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. 715--734, 2017.
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Finite functorial semi-norms and representability
( pdf ).
Also available at the arXiv:
1404.6557 [math.AT]
Published by
International Mathematics Research Notices, Volume 2016(12),
pp. 3616--3638, 2016.
The DOI is 10.1093/imrn/rnv250.
(pdf)
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Integral foliated simplicial volume of hyperbolic 3-manifolds
( 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. 825--865, 2016.
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Functorial semi-norms 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. 1453--1499, 2015.
The DOI is 10.2140/agt.2015.15.1453.
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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. 97--111, 2013.
The original publication is available at
www.springerlink.com.
The DOI is 10.1007/s10711-012-9761-x.
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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. 181--204, 2013.
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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. 457--470, 2009.
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Degree theorems and Lipschitz simplicial volume for non-positively
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. 193--225, 2009.
Also available through the
Journal of Topology Virtual Issue
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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. 545--561 2009.
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Isomorphisms in l^1-homology
( pdf, previous version ).
Also available at the
arXiv:
math.AT/0612589.
Münster Journal of
Mathematics
( pdf ),
Volume 1, pp. 237-266, 2008.
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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/s00209-005-0905-7. The complete reference of the
printed version is:
Mathematische Zeitschrift, Volume 253, Number 1, pp. 197-218, 2006.
preprints
other contributions/notes
implementation/formalisation of research work
-
Implementation/formalisation of teaching material is listed
here.
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.