NONTRIVIAL BAUMSLAG-SOLITAR RELATIONS IN EXTENDED ADMISSIBLE GROUPS

Modular functoriality for finite groups

We develop an extension of Deligne--Lusztig theory to certain (possibly infinite type) disconnected reductive groups arising from the special fibers of point stabilizers in the Bruhat--Tits building, which we call \emph{paraductive}. We then compute explicit lower bounds for the Tate cohomology of representations of pa...

From algebraic orthogonality to RAAG embedding obstructions in hierarchically hyperbolic groups

We introduce the $\textit{expanded core graph}$, which records minimal unbounded domains and their axial directions, for two classes of hierarchically hyperbolic group structures modeled on compact special groups and mapping class groups. Our main structural result shows that every embedding of a right-angled Artin gro...

Higher Kazhdan projections for one relator groups

We study the $K$-theory classes of higher Kazhdan projections of a discrete group under a spectral-gap assumption and recall how they are obtained, via the Baum--Connes assembly map, from equivariant Euler classes. After reviewing the case of virtually free groups, where the universal space for proper actions has a one...

Stability Patterns for Spherical and Projective Braid Groups

McDuff and Segal proved homological stability for unordered configuration spaces of connected manifolds with non-empty boundary. Later, Church proved representation stability for ordered configuration spaces on compact manifolds. These stability patterns extend to surface braid groups and pure surface braid groups, res...

Quantitative bordism over acyclic groups and Cheeger–Gromov (cid:26) -invariants

Groups of Transverse Stratifications and the Hierarchy of Configuration Spaces

We introduce a broad family of groups $G(\Gamma)$ associated with transverse stratifications of moduli spaces. For a wide class of stratifications satisfying a natural local condition (transverse niceness), we construct a homomorphism from the fundamental group of the moduli space to the corresponding group $G(\Gamma)$...