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Prof. Dr. Roman Sauer

Head of topology group
Office Hours: nach Vereinbarung
Room: 1.001
Phone: +49 (0) 721 608-46325
Fax: +49 (0) 721 608-42148
roman sauerHnq6∂kit edu

Karlsruher Institut für Technologie
MATH | IAG | AG Topologie
Englerstr. 2 | Mathebau (20.30)
76131 Karlsruhe

Publications | Roman Sauer


  • Bounded cohomology of amenable covers via classifying spaces
    joint with Clara Löh
    to appear in L’Enseignement Mathématique
  • Profinite invariants of arithmetic groups
    joint with Holger Kammeyer, Steffen Kionke and Jean Raimbault
    to appear in Forum of Mathematics, Sigma
  • S-arithmetic spinor groups with the same finite quotients and distinct l²-cohomology
    joint with Holger Kammeyer
    to appear in Groups, Geometry, and Dynamics
  • Homology and homotopy complexity in negative curvature
    joint with Uri Bader and Tsachik Gelander
    to appear in Journal of the European Mathematical Society


Research articles

  • Lattice Envelopes
    joint with Uri Bader and Alex Furman
    Duke Mathematical Journal (2020).
    [Journal] [arXiv:1711.08410]
  • Counting maximally broken Morse trajectories on aspherical manifolds
    joint with Caterina Campagnolo
    Geometriae Dedicata 202 (2019), 387–399.
    [Journal] [arXiv:1808.08737] [MR4001823]
  • An adelic arithmeticity theorem for lattices in products
    joint with Uri Bader and Alex Furman
    Math. Z. 293 (2019), no. 3-4, 1181–1199.
    [Journal] [arXiv:1705.08158] [MR4024582]
  • 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]
  • 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]
  • 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]


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]



  • The asymptotic growth of twisted torsion
    joint with Nicolas Bergeron and Wolfgang Lück









Conferences | Roman Sauer















































Talks | Roman Sauer


  • TU Dresden, Conference: Geometry and Approximation, August 2019
  • Cortona, Conference and summer school: Geometry of scalar curvature, July 2019
  • IMPAN Warsaw, Simons Semester: Geometric and Analytic Group Theory, June 2019



  • ICMAT Madrid, Workshop in the thematic program: l2-Betti numbers and their analogues in positive characteristic, June 2018



  • MFO Oberwolfach, Workshop on Geometric Structures in Group Theory, June 2017
  • Les Diablerets, PhD School on Growth in Geometry and Topology, August 2017







  • Sde Boker, Workshop on Generalized Cohomology, February 2015




  • MFO Oberwolfach, Arbeitstagung: Totally Disconnected Groups, October 2014
  • MPI Bonn, Homology Growth Seminar, February 2014




  • MFO Oberwolfach, Workshop: Group Theory, Measure, and Asymptotic Invariants, August 2013







  • Beit Hatfutsot, Tel Aviv, Transcending Tradition - Jewish Mathematicians in German-Speaking Academic Culture, November 2011
  • Technion, Haifa, Conference on Geometric Group Theory, June 2011




  • MFO Oberwolfach, Workshop: Actions and Invariants of Residually Finite Groups: Asymptotic Methods, September 2010
  • Technion, Haifa, Geometry Seminar, June 2010
  • ETH Zürich, Algebra and Topology Seminar, March 2010













  • MPI Bonn, Activity on Geometry and Group Theory, July 2006
  • CRM Montreal, Conference on Geometric Group Theory, July 2006
  • MFO Oberwolfach, Topological and Geometric Methods in Group Theory, April 2006







  • Luminy, Seminar, November 2004
  • Diablerets, Invariants sous Quasi-Isometrie, April 2004