Topics in Mathematics Münster

Research Interests

$\bullet$ Positive scalar curvature.
$\bullet$ Index theory, secondary index invariants.
$\bullet$ Cobordism categories and spaces of diffeomorphisms.
$\bullet$ Characteristic classes of manifold bundles.

Selected Publications of Prof. Dr. Johannes Ebert

$\bullet$ J. Ebert. The two definitions of the index difference. Trans. Amer. Math. Soc., 369(10):7469–7507, 2017.

$\bullet$ B. Botvinnik, J. Ebert, and O. Randal-Williams. Infinite loop spaces and positive scalar curvature. Invent. Math., 209(3):749–835, 2017.

$\bullet$ J. Ebert and O. Randal-Williams. Torelli spaces of high-dimensional manifolds. J. Topol., 8(1):38–64, 2015.

$\bullet$ J. Ebert and O. Randal-Williams. Generalised Miller- Morita- Mumford classes for block bundles and topological bundles. Algebr. Geom. Topol., 14(2):1181–1204, 2014.

$\bullet$ J. Ebert. A vanishing theorem for characteristic classes of odd-dimensional manifold bundles. J. Reine Angew. Math., 684:1–29, 2013.

$\bullet$ J. Ebert and O. Randal-Williams. Stable cohomology of the universal Picard varieties and the extended mapping class group. Doc. Math., 17:417–450, 2012.

$\bullet$ J. Ebert and J. Giansiracusa. Pontrjagin- Thom maps and the homology of the moduli stack of stable curves. Math. Ann., 349(3):543–575, 2011.

$\bullet$ J. Ebert. Algebraic independence of generalized {MMM}-classes. Algebr. Geom. Topol., 11(1):69–105, 2011.

$\bullet$ J. Ebert. The icosahedral group and the homotopy of the stable mapping class group. Münster J. Math., 3:221–231, 2010.

$\bullet$ J. Ebert and J. Giansiracusa. {On the homotopy type of the Deligne- Mumford compactification}. Algebr. Geom. Topol., 8(4):2049–2062, 2008.

Current Cluster Publications of Prof. Dr. Johannes Ebert

$\bullet $ Johannes Ebert and Michael Wiemeler. On the homotopy type of the space of metrics of positive scalar curvature. Journal of the European Mathematical Society, 26(9):3327–3363, July 2024. doi:10.4171/JEMS/1333.

$\bullet $ Johannes Ebert. Tautological classes and higher signatures. arXiv e-prints, March 2024. arXiv:2403.02755.

$\bullet $ Johannes Ebert and Jens Reinhold. Some rational homology computations for diffeomorphisms of odd‐dimensional manifolds. Journal of Topology, January 2024. doi:10.1112/topo.12324.

$\bullet $ Johannes Ebert. Diffeomorphisms of odd-dimensional discs, glued into a manifold. Algebraic & Geometric Topology, 23(5):2329–2345, July 2023. doi:10.2140/agt.2023.23.2329.

$\bullet $ Boris Botvinnik and Johannes Ebert. Positive scalar curvature and homotopy theory. In Perspectives in Scalar Curvature, pages 83–157. World Scientific, March 2023. doi:10.1142/9789811273230_0003.

$\bullet $ Johannes Ebert and Oscar Randal-Williams. The positive scalar curvature cobordism category. Duke Math. J., 171(11):2275–2406, August 2022. doi:10.1215/00127094-2022-0023.

$\bullet $ Johannes Ebert and Jens Reinhold. Some rational homology computations for diffeomorphisms of odd-dimensional manifolds. arXiv e-prints, March 2022. arXiv:2203.03414.

$\bullet $ Johannes Ebert and Georg Frenck. The gromov-lawson-chernysh surgery theorem. Boletín de la Sociedad Matemática Mexicana, 27(2):37, March 2021. doi:10.1007/s40590-021-00310-w.

$\bullet $ Boris Botvinnik, Johannes Ebert, and David J. Wraith. On the topology of the space of Ricci-positive metrics. Proc. Amer. Math. Soc., 148:3997–4006, April 2020. doi:10.1090/proc/14988.

$\bullet $ Johannes Ebert and Oscar Randal-Williams. Semisimplicial spaces. Algebr. Geom. Topol., 19(4):2099–2150, August 2019. doi:10.2140/agt.2019.19.2099.

$\bullet $ Johannes Ebert and Oscar Randal-Williams. Infinite loop spaces and positive scalar curvature in the presence of a fundamental group. Geom. Topol., 23(3):1549–1610, May 2019. doi:10.2140/gt.2019.23.1549.

$\bullet $ Johannes Ebert. Index theory in spaces of manifolds. Math. Ann., 374(1-2):931–962, January 2019. doi:10.1007/s00208-019-01809-4.