Research Group Geometry, Topology and Group theory

Mathematisches Institut, Universität Münster

# Research

#### Research interests of the group include

• Geometry: Tits buildings, symmetric spaces, nonpositive curvature, metric geometry, isoparametric submanifolds.
• Groups: Geometric group theory, Lie groups, transformation groups, isometric actions, algebraic groups, classical groups.
• Topology: Geometric topology, homogeneous spaces, group cohomology.

#### Postdocs

• Dr. Rupert McCallum
• Dr. Petra Schwer
• Dr. Daniel Skodlerack
• Dr. Stefan Witzel

#### Current PhD Projects

• Antoine Beljean
• Olga Varghese

#### Research Grants and Funding

• SFB 878 Project B4 Reductive groups and combinatorial structures (Kramer)
• DFG Project Exceptional groups and geometrical structures (Kramer and Weiss)
• DFG Project Hadamard spaces: rigidity and recognition theorems (Schwer)
• Promotionsstipendien: DAAD, Studienstiftung des Deutschen Volkes, Telekom-Stiftung

#### Current Research Projects

• Structure of nondiscrete affine buildings (Kramer, Schwer, Beljean)
• Cubical complexes and systolic geometry (Schwer)
• Embeddings between Bruhat-Tits Buildings (Skodlerack)
• Lattices and geometric group theory (Witzel)
• Buildings and topological groups (McCallum, Kramer)
• Actions of Aut(Fn) (Varghese)
• Buildings and group cohomology (Kramer)
• Buildings and exceptional groups (Kramer joint with R. Weiss)
• Classification of isoparametric hypersurfaces (Kramer joint with S. Stolz)

#### Preprints from our group

1. M. Fluch, S. Witzel, Brown's criterion in Bredon homology.
Preprint.
2. S. Witzel, Abels's groups revisited.
Preprint.
3. M. Fluch, M. Schwandt, S. Witzel, M.C.B. Zaremsky, The Brin-Thompson groups sV are of type F.
Preprint.
4. O. Varghese, Fixed points for actions of Aut(Fn) on CAT(0) spaces.
Submitted.
5. D. Skodlerack, On intertwining implies conjugacy for classical groups.
Preprint.
6. D. Skodlerack, Embeddings of local fields in simple algebras and simplicial structures on the Bruhat-Tits building.
Submitted.
7. D. Skodlerack, Field Embeddings which are conjugate under a unit of a p-adic classical Group.
Preprint.
8. J. Essert, On Wagoner complexes.
Submitted.
9. F. Magata, An integration formula for polar actions.
Preprint.
10. L. Kramer, Notes on completely reducible subcomplexes of spherical buildings.
Lecture notes from April 2008.

#### Publications from our group since 2010

1. L. Kramer, R. Weiss, Coarse equivalences of Euclidean buildings.
Adv. Math. 253 (2014), no 1, 1-49.
2. J. Essert, A geometric construction of panel-regular lattices in buildings of types $$\tilde A_2$$ and $$\tilde C_2$$.
Algebr. Geom. Topol. 13 (2013), no. 3, 1531–1578.
3. K.H. Hofmann, L. Kramer, Transitive actions of locally compact groups on locally contractible spaces.
To appear in J. Reine Angew. Mathematik.
4. J. Essert, Homological stability of classical groups.
Israel J. Math. 198 (2013), no. 1, 169–204.
5. R. McCallum, A local-to-global result for topological spherical buildings.
Adv. Geom. 13 (2013), no. 3, 435–448.
6. K.-U. Bux, R. Köhl, S. Witzel, Higher finiteness properties of reductive arithmetic groups in positive characteristic: the Rank Theorem.
Ann. of Math. (2) 177 (2013), no. 1, 311–366.
7. D. Skodlerack, The centralizer of a classical group and Bruhat Tits buildings.
Ann. Inst. Fourier (Grenoble) 63 (2013), no. 2, 515–546.
8. T. Grundhofer, L. Kramer, H. Van Maldeghem, R. M. Weiss, Compact totally disconnected Moufang buildings.
Tohoku Math. Journal 64 (2012) no 3.
9. R. Köhl, S. Witzel, The sphericity of the Phan geometries of type Bn and Cn and the Phan-type theorem of type F4.
To appear in Transactions AMS.
10. P. Schwer, K. Struyve, Λ-buildings and base change functors.
Geom. Dedicata, 157 (2012) 291 - 317.
11. L. Kramer, Metric properties of euclidean buildings.
In: Global Differential Geometry, Springer Proceedings in Mathematics, Volume 17 (2012).
12. L. Kramer, The topology of a semisimple Lie group is essentially unique.
Adv. Math. 228 (2011), no. 5, 2623-2633.
13. L. Kramer, On the local structure and the homology of CAT(κ) spaces and euclidean buildings.
Advances in Geometry 11 (2011), 347-369.
14. P. Hitzelberger, Non-discrete affine buildings and convexity.
Advances in Mathematics, 227 (2011) 210 - 244.
15. T. Kurth, R. Gramlich and L. Kramer, The real quadrangle of type E6.
Advances in Geometry 11 (2011), 347-369.
16. E. Bornberg-Bauer and L. Kramer, Robustness versus evolvability: a paradigm revisited.
HFSP J. Volume 4, Issue 3, pp. 105-108, 2010/06.
17. F. Magata, A general Weyl-type Integration Formula for Isometric Group Actions.
Transformation Groups 15, no. 1 (2010).
18. P. Hitzelberger, L. Kramer, R. Weiss, Non-discrete Euclidean Buildings for the Ree and Suzuki groups.
Amer. J. Math 132, no. 4 (2010).
19. L. Kramer and K. Tent, A Maslov cocycle for unitary groups..
Proc. London Math. Soc. 100, no. 3 (2010), 91-115.
20. P. Hitzelberger, Kostant convexity for affine buildings.
Forum Mathematicum, vol. 22, no. 5 (2010) 959-971.