Research

My main research areas are transformation groups, geometric structures on manifolds, and geometric and differential topology.

Topics

• GKM manifolds and GKM graphs
• Hamiltonian non-Kähler actions
• Symplectic and Kähler structures on biquotients
• Geometric and topological invariants for maps from manifolds into spheres
• Geometric and topological invariants for vector bundles over manifolds
• Topological properties of G-structures on manifolds
• Cappuccino spectra

Preprints

• 2026
  On orientability, Poincaré duality, and connectivity of GKM graphs. With O. Goertsches and L. Zoller. arXiv:2608.26999
• 2026
  Finiteness and boundedness of positive monotone Hamiltonian GKM₃ spaces. With S. Sabatini and L. Zoller. arXiv:2606.28768
• 2026
  Almost quaternionic structures on compact rank one symmetric spaces. With O. Goertsches, E. Loiudice and G. Solomadin. arXiv:2606.12659
• 2025
  On torus equivariant S⁴-bundles over S⁴ and Petrie-type questions for GKM-manifolds. With O. Goertsches and L. Zoller. arXiv:2509.03100
• 2025
  On GKM fiber bundles and realizability with full flag fibers. With O. Goertsches, N. Wardenski and L. Zoller. arXiv:2504.15662
• 2022
  The GKM correspondence in dimension 6. With O. Goertsches and L. Zoller. arXiv:2210.01856

Publications

• 2025
  Exotic almost complex circle actions on 6-manifolds. With N. Lindsay. Ann. Global Anal. Geom. 68, 7 (2025). arXiv:2308.06832
• 2024
  GKM theory in low dimensions. With O. Goertsches and L. Zoller. In: Group actions and equivariant cohomology, Contemp. Math. 808 (2024), 113–146. arXiv:2210.06234
• 2024
  On the Stiefel–Whitney classes of GKM manifolds. With O. Goertsches and L. Zoller. C. R. Math. Acad. Sci. Soc. R. Can. 46 (2024), no. 2, 16–40. arXiv:2401.00528
• 2023
  Realization of GKM fibrations and new examples of Hamiltonian non-Kähler actions. With O. Goertsches and L. Zoller. Compos. Math. 159 (2023), no. 10, 2149–2190.
• 2022
  GKM manifolds are not rigid. With O. Goertsches and L. Zoller. Algebr. Geom. Topol. 22 (2022), no. 7, 3511–3532. arXiv:2007.13620
• 2021
  Vector bundles and cohomotopies of spin 5-manifolds. Homology Homotopy Appl. 23 (2021), no. 1, 143–158. arXiv:1812.06547
• 2020
  A counting invariant for maps into spheres and for zero loci of sections of vector bundles. Abh. Math. Semin. Univ. Hambg. 90 (2020). arXiv:1911.03214
• 2020
  GKM theory and Hamiltonian non-Kähler actions in dimension 6. With O. Goertsches and L. Zoller. Adv. Math. 368 (2020), 107141. arXiv:1903.11684
• 2020
  Symplectic and Kähler structures on biquotients. With O. Goertsches and L. Zoller. J. Symplectic Geom. 18 (2020), no. 3, 791–813. arXiv:1812.09689
• 2019
  Almost complex structures on connected sums of complex projective spaces. With O. Goertsches. Ann. K-Theory 4 (2019), no. 1, 139–149. arXiv:1710.05316
• 2018
  The Hopf problem on the (non-)existence of complex structures on S⁶. With I. Agricola, G. Bazzoni, O. Goertsches and S. Rollenske. Differential Geom. Appl. 57 (2018), 1–9. arXiv:1708.01068
• 2018
  Almost complex structures on spheres. With M. Parton. Differential Geom. Appl. 57 (2018), 10–22. arXiv:1707.03883
• 2018
  On the existence of an irreducible SO(3)-structure on five-manifolds. Topology Appl. 239 (2018), 81–91. arXiv:1508.06150
• 2016
  A classification of isometry groups of homogeneous 3-manifolds. With F. Loose. Math. Nachr. 289 (2016), no. 13, 1648–1664. doi:10.1002/mana.201400292

Theses

• 2013
  Three-dimensional homogeneous spaces and their application in general relativity. Dissertation, Eberhard Karls Universität Tübingen.
• 2008
  Perelmans Monotonieformel für das reduzierte Volumen. Diplomarbeit, Eberhard Karls Universität Tübingen.

Other

• 2014
  Bianchi's classification of 3-dimensional Lie algebras revisited. With M. Glas, A. Krause and F. Loose. arXiv:1403.2278
  We revisit L. Bianchi's original proof of the classification of 3-dimensional Lie algebras in modern mathematical language.