Publications

Book projects

• L2-Invariants - n years after (working title)
  Wolfgang Lück, Roman Sauer, Thomas Schick, 2030 [link].

• Metric topology of aspherical manifolds (MFO seminar series)
  Clara Löh, Roman Sauer, 2025 [link].

Preprints

• Higher property T and below-rank phenomena of lattices
  Uri Bader, Roman Sauer
  arxiv:2511.20192, 2025. [arXiv]

• The cheap embedding principle: Dynamical upper bounds for homology growth
  Kevin Li, Clara Löh, Marco Moraschini, Roman Sauer, Matthias Uschold
  arxiv:2508.01347, 2025. [arXiv]

• Uniform waist inequalities in codimension two for manifolds with Kazhdan fundamental group
  Uri Bader, Roman Sauer
  arxiv:2407.19783, 2024. [arXiv]

• Higher Kazhdan property and unitary cohomology of arithmetic groups
  Uri Bader, Roman Sauer
  arxiv:2308.06517, 2023. [arXiv]

Published

• The algebraic cheap rebuilding property
  Kevin Li, Clara Löh, Marco Moraschini, Roman Sauer, Matthias Uschold
  to appear in Transactions of the American Mathematical Society., 2025. [Journal] [arXiv] [MathSciNet]

• On homological properties of the Schlichting completion
  Laura Bonn, Roman Sauer
  Mathematical Proceedings of the Cambridge Philosophical Society, 2025. [Journal] [arXiv] [MathSciNet]

• Stability and instability of lattices in semisimple groups
  Uri Bader, Alexander Lubotzky, Roman Sauer, Shmuel Weinberger
  J. Anal. Math., 2023. [Journal] [arXiv] [MathSciNet]

• Amenable covers and integral foliated simplicial volume
  Clara Löh, Marco Moraschini, Roman Sauer
  New York J. Math., 2022. [Journal] [arXiv] [MathSciNet]

• Volume and macroscopic scalar curvature
  Sabine Braun, Roman Sauer
  Geom. Funct. Anal., 2021. [Journal] [arXiv] [MathSciNet]

• Profinite invariants of arithmetic groups
  Holger Kammeyer, Steffen Kionke, Jean Raimbault, Roman Sauer
  Forum Math. Sigma, 2020. [Journal] [arXiv] [MathSciNet]

• S-arithmetic spinor groups with the same finite quotients and distinct ℓ²-cohomology
  Holger Kammeyer, Roman Sauer
  Groups Geom. Dyn., 2020. [Journal] [arXiv] [MathSciNet]

• Bounded cohomology of amenable covers via classifying spaces
  Clara Löh, Roman Sauer
  Enseign. Math., 2020. [Journal] [arXiv] [MathSciNet]

• Homology and homotopy complexity in negative curvature
  Uri Bader, Tsachik Gelander, Roman Sauer
  J. Eur. Math. Soc. (JEMS), 2020. [Journal] [arXiv] [MathSciNet]

• Lattice envelopes
  Uri Bader, Alex Furman, Roman Sauer
  Duke Math. J., 2020. [Journal] [arXiv] [MathSciNet]

• An adelic arithmeticity theorem for lattices in products
  Uri Bader, Alex Furman, Roman Sauer
  Math. Z., 2019. [Journal] [arXiv] [MathSciNet]

• Counting maximally broken Morse trajectories on aspherical manifolds
  Caterina Campagnolo, Roman Sauer
  Geom. Dedicata, 2019. [Journal] [arXiv] [MathSciNet]

• Vanishing of ℓ²-Betti numbers of locally compact groups as an invariant of coarse equivalence
  Roman Sauer, Michael Schrödl
  Fund. Math., 2018. [Journal] [arXiv] [MathSciNet]

• ℓ²-Betti number of discrete and non-discrete groups
  Roman Sauer
  London Math. Soc. Lecture Note Ser., 447 (Book chapter), 2018. [Journal] [arXiv] [MathSciNet]

• ℓ²-Betti numbers of totally disconnected groups and their approximation by Betti numbers of lattices
  Henrik Densing Petersen, Roman Sauer, Andreas Thom
  J. Topol., 2018. [Journal] [arXiv] [MathSciNet]

• Topological models of finite type for tree almost automorphism groups
  Roman Sauer, Werner Thumann
  Int. Math. Res. Not. IMRN, 2017. [Journal] [arXiv] [MathSciNet]

• Cantor systems and quasi-isometry of groups
  Kostya Medynets, Roman Sauer, Andreas Thom
  Bull. Lond. Math. Soc., 2017. [Journal] [arXiv] [MathSciNet]

• Integral foliated simplicial volume of aspherical manifolds
  Roberto Frigerio, Clara Löh, Cristina Pagliantini, Roman Sauer
  Israel J. Math., 2016. [Journal] [arXiv] [MathSciNet]

• Volume and homology growth of aspherical manifolds
  Roman Sauer
  Geom. Topol., 2016. [Journal] [arXiv] [MathSciNet]

• On the structure and arithmeticity of lattice envelopes
  Uri Bader, Alex Furman, Roman Sauer
  C. R. Math. Acad. Sci. Paris, 2015. [Journal] [arXiv] [MathSciNet]

• ℓ²-invisibility and a class of local similarity groups
  Roman Sauer, Werner Thumann
  Compos. Math., 2014. [Journal] [arXiv] [MathSciNet]

• On the growth of Betti numbers in p-adic analytic towers
  Nicolas Bergeron, Peter Linnell, Wolfgang Lück, Roman Sauer
  Groups Geom. Dyn., 2014. [Journal] [arXiv] [MathSciNet]

• Weak notions of normality and vanishing up to rank in ℓ²-cohomology
  Uri Bader, Alex Furman, Roman Sauer
  Int. Math. Res. Not. IMRN, 2014. [Journal] [arXiv] [MathSciNet]

• On the cohomology of weakly almost periodic group representations
  Uri Bader, Christian Rosendal, Roman Sauer
  J. Topol. Anal., 2014. [Journal] [arXiv] [MathSciNet]

• Integrable measure equivalence and rigidity of hyperbolic lattices
  Uri Bader, Alex Furman, Roman Sauer
  Invent. Math., 2013. [Journal] [arXiv] [MathSciNet]

• Efficient subdivision in hyperbolic groups and applications
  Uri Bader, Alex Furman, Roman Sauer
  Groups Geom. Dyn., 2013. [Journal] [arXiv] [MathSciNet]

• Spectral distribution and ℓ²-isoperimetric profile of Laplace operators on groups
  Alexander Bendikov, Christophe Pittet, Roman Sauer
  Math. Ann., 2012. [Journal] [arXiv] [MathSciNet]

• Euler characteristics of categories and homotopy colimits
  Fiore, Thomas M., Wolfgang Lück, Roman Sauer
  Doc. Math., 2011. [Journal] [arXiv] [MathSciNet]

• Finiteness obstructions and Euler characteristics of categories
  Thomas M. Fiore, Wolfgang Lück, Roman Sauer
  Adv. Math., 2011. [Journal] [arXiv] [MathSciNet]

• The limit of F_p-Betti numbers of a tower of finite covers with amenable fundamental groups
  Peter Linnell, Wolfgang Lück, Roman Sauer
  Proc. Amer. Math. Soc., 2011. [Journal] [arXiv] [MathSciNet]

• ℓ²-torsion, the measure-theoretic determinant conjecture, and uniform measure equivalence
  Wolfgang Lück, Roman Sauer, Christian Wegner
  J. Topol. Anal., 2010. [Journal] [arXiv] [MathSciNet]

• A spectral sequence to compute ℓ²-Betti numbers of groups and groupoids
  Roman Sauer, Andreas Thom
  J. Lond. Math. Soc. (2), 2010. [Journal] [arXiv] [MathSciNet]

• Amenable covers, volume and ℓ²-Betti numbers of aspherical manifolds
  Roman Sauer
  J. Reine Angew. Math., 2009. [Journal] [arXiv] [MathSciNet]

• Simplicial volume of Hilbert modular varieties
  Clara Löh, Roman Sauer
  Comment. Math. Helv., 2009. [Journal] [arXiv] [MathSciNet]

• Degree theorems and Lipschitz simplicial volume for nonpositively curved manifolds of finite volume
  Clara Löh, Roman Sauer
  J. Topol., 2009. [Journal] [arXiv] [MathSciNet]

• Volume and ℓ²-Betti numbers of aspherical manifolds
  Roman Sauer
  Trends in mathematics. Proceedings of the Courant Colloquium, University of Göttingen, 2008. [Journal] [arXiv] [MathSciNet]

• Homological invariants and quasi-isometry
  Roman Sauer
  Geom. Funct. Anal., 2006. [Journal] [arXiv] [MathSciNet]

• ℓ²-Betti numbers of discrete measured groupoids
  Roman Sauer
  Internat. J. Algebra Comput., 2005. [Journal] [arXiv] [MathSciNet]

• Power series over the group ring of a free group and applications to Novikov-Shubin invariants
  Roman Sauer
  Proceedings of the School, ICTP, Trieste, on High-dimensional manifold topology, 2003. [Journal] [arXiv] [MathSciNet]