# Preprints

*Profinite invariants of arithmetic groups*

joint with Holger Kammeyer, Steffen Kionke and Jean Raimbault

[arXiv:1901.01227]

*S-arithmetic spinor groups with the same finite quotients and distinct l²-cohomology*

joint with Holger Kammeyer

to appear in Groups, Geometry, and Dynamics

[arXiv:1804.10604]

*Lattice Envelopes*

joint with Uri Bader and Alex Furman

to appear in Duke Mathematical Journal

[arXiv:1711.08410]

*Homology and homotopy complexity in negative curvature*

joint with Uri Bader and Tsachik Gelander

to appear in Journal of the European Mathematical Society

[arXiv:1612.04871]

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# Research articles

*Counting maximally broken Morse trajectories on aspherical manifolds*

joint with Caterina Campagnolo

Geometriae Dedicata (2019)

[Journal][arXiv:1808.08737]

*An adelic arithmeticity theorem for lattices in products*

joint with Uri Bader und Alex Furman

Math. Z. (2019)

[Journal][arXiv:1705.08158]

*Vanishing of l²-Betti numbers of locally compact groups as an invariant of coarse equivalence*

joint with Michael Schrödl

Fund. Math. 243 (2018), no. 3, 301–311.

[arXiv:1702.01685] [Journal] [MR3863061]

*l²-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices*

joint with Henrik D. Petersen and Andreas Thom

J. Topol. 11 (2018), no. 1, 257–282.

[arXiv:1612.04559] [Journal] [MR3784232]

*Cantor systems and quasi-isometry of groups*

joint with Kostya Medynets and Andreas Thom

Bulletin of the LMS 49 (2017), no. 4, 709–724

[arXiv:1508.07578] [Journal] [MR3725491]

*Topological models of finite type for tree almost automorphism groups*

joint with Werner Thumann

Int. Math. Res. Not. IMRN 2017, no. 23, 7292–7320.

[arXiv: 1510.05554] [Journal] [MR3801421]

*Integral foliated simplicial volume of aspherical manifolds*

joint with Roberto Frigerio and Clara Löh and Cristina Pagliantini

Israel J. Math. 216 (2016), no. 2, 707–751

[arXiv:1506.05567] [Journal] [MR3557463]

*Volume and homology growth of aspherical manifolds*

Geom. Topol. 20 (2016), 1035-1059

[arXiv: 1403.7319] [Journal] [MR3493098]

*On the structure and arithmeticity of lattice envelopes*

joint with Uri Bader and Alex Furman

C. R. Math. Acad. Sci. Paris 353 (2015), no. 5, 409–413.

[arXiv:1411.7332] [Journal] [MR3334993]

*L²-invisibility and a class of local similarity groups*

joint with Werner Thumann

Compositio Math.150 (2014), no. 10, 1742-1754

[arXiv:1304.6843] [Journal] [MR3269466]

*On the growth of Betti numbers in p-adic analytic towers*

joint with Nicolas Bergeron and Peter Linnell and Wolfgang Lück

Groups Geom. Dyn. 8 (2014), no. 2, 311–329

[arXiv:1204.3298] [Journal] [MR3231217]

*Weak notions of normality and vanishing up to rank in L²-cohomology*

joint with Uri Bader and Alex Furman

Int. Math. Res. Not. IMRN 2014, no. 12, 3177–3189

[arXiv:1206.4793] [Journal] [MR3217658]

*On the cohomology of weakly almost periodic group representations*

joint with Uri Bader and Christian Rosendal

Journal of Topology and Analysis 6 (2014), no. 2, 153-165

[arXiv:1302.1392] [Journal] [MR3191647]

*Integrable measure equivalence and rigidity of hyperbolic lattices*

joint with Uri Bader and Alex Furman

Inventiones Math. 194 (2013), No. 2, 313–379

[arXiv:1006.5193] [Journal] [MR3117525]

*Efficient subdivision in hyperbolic groups and applications*

joint with Uri Bader and Alex Furman

Groups, Geometry, and Dynamics 7 (2013), 263-292

[arXiv:1003.1562] [Journal] [MR3054570]

*Euler characteristics of categories and homotopy colimits*

joint with Tom Fiore and Wolfgang Lück

Documenta Math. 16 (2011), 301-354

[arXiv:1007.3868] [Journal] [MR2804514]

*Spectral distribution and L²-isoperimetric profile of Laplace operators on groups*

joint with Alexander Bendikov and Christophe Pittet

Mathematische Annalen 354 (2012), 43-72

[arXiv:0901.0271] [Journal] [MR2957618]

*Finiteness obstructions and Euler characteristics of categories*

joint with Tom Fiore and Wolfgang Lück

Advances in Mathematics 226 (2011), no. 3, 2371–2469

[arXiv:0908.3417] [Journal] [MR2739781]

*The limit of F_p-Betti numbers of a tower of finite covers with amenable fundamental groups*

joint with Peter Linnell and Wolfgang Lück

Proc. Amer. Math. Soc. 139 (2011), 421-434

[arXiv:1003.0434] [Journal] [MR2736326]

*L²-torsion, the measure-theoretic determinant conjecture, and uniform measure equivalence*

joint with Wolfgang Lück and Christian Wegner

Journal of Topology and Analysis 2 (2010), no. 2, 145-171

[arXiv:0903.2925] [Journal] [MR2652905]

*A spectral sequence to compute L²-Betti numbers of groups and groupoids*

joint with Andreas Thom

Journal of the London Mathematical Society 81 (2010), no. 3, 747-773

[arXiv:0707.0906] [Journal] [MR2650795]

*Degree theorems and Lipschitz simplicial volume for non-positively curved manifolds of finite volume*

joint with Clara Löh

Journal of Topology 2 (2009), no. 1, 193-225

[arXiv:0710.1635] [Journal] [MR2499443]

*Simplicial Volume of Hilbert modular varieties*

joint with Clara Löh

Commentarii Mathematici Helvetici 84 (2009), no. 3, 457-470

[arXiv:0706.3904] [Journal] [MR2507250]

*Amenable covers, volume and L²-Betti numbers of aspherical manifolds*

J. Reine Angew. Math (Crelle's Journal) 636 (2009), 47-92

[math.AT/0605627] [Journal] [MR2572246]

*Homological invariants and quasi-isometry*

Geom. Funct. Anal. (GAFA) 16 (2006), no. 2, 476–515

[math.AT/0312129] [Journal] [MR2231471]

*L²-Betti numbers of discrete measured groupoids*

Internat. J. Algebra Comput. 15 (2005), no. 5-6, 1169–1188

[math.AT/0312411] [Journal] [MR2197826]

*Power series over the group ring of a free group and applications to Novikov-Shubin invariants*

Proceedings of the School High-Dimensional Manifold Topology, Trieste, 2003.

[pdf] [MR2048733]

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# Expository articles

*l²-Betti numbers of discrete and non-discrete groups*

in: London Mathematical Society Lecture Note Series 447, Cambridge University Press 2018

[arXiv:1509.05234] [Journal] [MR3793289]

*Homotopy invariance of almost flat Betti numbers*

joint with Thomas Schick

Enseign. Math. (2) 54 (2008), no. 1-2 (Guido's book of conjectures)

[pdf] [MR2454697]

*Volume and L²-Betti numbers of aspherical manifolds*

Proceedings of the Courant Colloquium Göttingen 2007 (ISBN 3-978-3-940344-56-4)

[Online edition] [pdf] [MR2906042]

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# Miscellaneous

*The asymptotic growth of twisted torsion*

joint with Nicolas Bergeron and Wolfgang Lück

[pdf]

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