Projects in Mathematics Muenster

Research area B: Spaces and Operators
Unit B2: Topology

Further Projects
CRC 1442: Geometry: Deformation and Rigidity - B03: Moduli spaces of metrics of positive curvature In this project, the space of Riemannian metrics of positive scalar curvature on closed manifolds will be studied. Central research questions concern the nontriviality of secondary index invariants, rigidity theorems for the homotopy type of those spaces and the action of the diffeomorphism group, and the comparison of two iterated loop space structures. We will use techniques from differential geometry, higher index theory, metric geometry, differential topology and homotopy theory. online
CRC 1442: Geometry: Deformation and Rigidity - C01: Automorphisms and embeddings of manifolds This project concerns the homotopical properties of spaces of smooth and topological automorphisms of manifolds, their classifying spaces and spaces of smooth and topological embeddings of manifolds. Known characteristic classes for manifold bundles will play an important role. It is conceivable that new ones will be constructed. The action of automorphisms and embeddings on finite subsets of manifolds, more precisely on the configuration category of a manifold, will be exploited. online

Research Interests

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

Selected Publications of 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 Publications

$\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. Diffeomorphisms of odd-dimensional discs, glued into a manifold. arXiv e-prints, July 2021. arXiv:2107.00903.

$\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 $ Johannes Ebert and Michael Wiemeler. On the homotopy type of the space of metrics of positive scalar curvature. arXiv e-prints, December 2020. arXiv:2012.00432.

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

$\bullet $ Johannes Ebert and Oscar Randal-Williams. Semisimplicial spaces. Algebraic & Geometric Topology, 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. Geometry and Topology, 23(3):1549–1610, May 2019. doi:10.2140/gt.2019.23.1549.

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