36. NRW Topology Meeting

BONN (GERMANY)

Thursday/Friday, November 6/7, 2025

No registration is necessary to participate in the 36. NRW Topology meeting, but registration is needed for dinner.

^*If you want to participate in the dinner on November 6, you need to register in advance by October 22 by email to Gunder Sievert ("gunder-lily.sievert(at)hcm.uni-bonn.de").

Some hotels in walking distance to the Mathematikzentrum that we recommend are: Best Western President, Motel One Bonn-Hauptbahnhof, InterCity Hotel.

How to get to the Mathematikzentrum. List of previous NRW Topology meetings.

ABSTRACTS

Grigori Avramidi (Bonn): A cellular waist inequality for hyperbolic manifolds
I will describe a result showing for a closed hyperbolic manifold M and a map f:M⟶ℝ^m, that there is a fiber whose topological complexity (measured by the number of cells in a cell structure) is bounded below in terms of the injectivity radius of M. This answers a recent question of Gromov. Joint work with Thomas Delzant.

Emma Brink (Bonn University): Equivariant bordism and Thom spectra
In this talk, we explore the relation between bordism theories and Thom spectra in equivariant homotopy theory. For a compact Lie group G, we describe a version of G-equivariant geometric bordism with respect to a given stable tangential structure. Equivariant bordism admits a Thom-Pontryagin comparison map to the homology theory represented by the associated Thom spectrum. The main result is that the Thom-Pontryagin map is an isomorphism when the connected component of G is central - for example if G is a product of a finite group and a torus. And when G is not of this type, geometric bordism is not represented by a genuine G-spectrum as it fails to admit certain Wirthmüller isomorphisms. This extends work of tom Dieck and Schwede for unoriented bordism to very general tangential structures. If time permits, we explain that for a multiplicative tangential structure such that all orbits are orientable, the Thom-Pontryagin map becomes an isomorphism after localizing its source and target at a family of inverse Thom classes.

Benjamin Brück (Münster University): (Non)-vanishing of high-dimensional group cohomology
A conjecture by Church-Farb-Putman predicts that the rational cohomology of SL_n(ℤ) vanishes in high degrees. I will talk about the current status of this conjecture and about techniques that have been used to obtain partial solutions to it. I will then give an overview of analogous (non-)vanishing results for the cohomology of related groups and moduli spaces.

Victor Saunier (Bielefeld University): A model for the assembly map of bordism-invariant functors
In joint work with Jordan Levin and Guglielmo Nocera, we give a model of the assembly of bordism-invariant, Karoubi-localizing functor of Poincaré categories which is a Verdier projection. In particular, we are able to control the kernel of the assembly map for L-theory with <-∞> decoration. Our proof relies on a careful analysis of when oplax colimits in Poincaré categories exist and are computed as in hermitian categories.

Claudia Scheimbauer (TU München): TBA

Julia Semikina (Université Lille): Scissors congruence K-theory for equivariant manifolds
The generalized Hibert's third problem asks about the invariants preserved under the scissors congruence operation: given a polytope P in ℝⁿ, one can cut P into a finite number of smaller polytopes and reassemble these to form Q. Kreck, Neumann and Ossa introduced and studied an analogous notion of cut-and-paste relation for manifolds called the SK-equivalence ("schneiden und kleben" is German for "cut and paste"). We introduce a scissors congruence K-theory spectrum which lifts the equivariant SK-groups for compact G-manifolds with boundary, and we show that on π₀ this is the source of a spectrum level lift of the Burnside ring valued equivariant Euler characteristic of a compact G-manifold. We also discuss a Mackey functor structure on equivariant SK-groups, which is a shadow of a higher genuine equivariant structure.

Georg Tamme (Mainz University): Localizing invariants of pushouts and non-commutative Hodge theory
The singular cohomology of a smooth, proper complex variety carries a pure Hodge structure consisting of a rational lattice given by singular cohomology with rational coefficients and a Hodge filtration on cohomology with complex coefficients coming from the comparison with de Rham cohomology, these two structures interacting in a specific way. Katzarkov, Kontsevich, and Pantev conjecture that this should generalize to non-commutative smooth, proper varieties, i.e. to smooth, proper ℂ-linear stable ∞-categories. In this case, de Rham cohomology is replaced by periodic cyclic homology, and the rational lattice is conjecturally given by Toën's and Blanc's topological K-theory. As Deligne constructed a mixed Hodge structure on the singular cohomology of arbitrary complex varieties, one may also ask what happens for not necessarily smooth or proper ℂ-linear stable ∞-categories. In this talk, I will indicate how results about localizing invariants on pushouts of rings can be used to prove some cases of the lattice conjecture, for example for certain group rings. Most of these results have also been obtained by different techniques by Konovalov. This is joint work with Markus Land.

Thomas Willwacher (ETH Zürich): Models for configuration spaces of points via obstruction theory
Consider the (Fulton-MacPherson-)configuration spaces of r distinguishable points on a manifold M, FM_M(r). If M is parallelized, the collection FM_M is a module over the Fulton-MacPherson operad FM_n. One then desires to find an algebraic model of FM_M in the sense of rational homotopy theory. In prior work this has been done by analytic methods using configuration space integrals. We discuss a different approach using algebraic obstruction theory alone. More precisely, in the rational setting, one can classify all operadic right FM_n modules of configuration space type, and in good cases there are so few that the correct one may be identified. The talk is based on my paper arXiv:2302.07369 and extensions in joint works in progress with Florian Naef and Silvan Schwarz.