Aug 2026· 1 citation· ⚡ 1 influential· 30 references
Mathematics
Abstract
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 group, after replacing its standard generators by positive powers, factors through an intermediate RAAG generated by suitably supported axial elements; for the class modeled on compact special groups, this intermediate RAAG is quasi-isometrically embedded. We show that its extension graph embeds into the expanded core graph. This yields a Kim--Koberda-type obstruction to RAAG embeddings and a complete embedding criterion when the rank is at most two. For the standard HHG structure on a mapping class group, the expanded core graph is the disjointness graph of essential curves, while for natural rich-family structures on a RAAG it recovers the extension graph. We also establish permanence results under finite direct products and the standard relatively hyperbolic construction.
We study when, and how compactly, a finite connected graph (G) embeds isometrically into a Cayley graph of a finite abelian group. The classical theory of partial cubes answers this for isometric subgraphs of hypercubes through the Djokovic-Winkler relation (\theta); we extend the question to the full family of abelian...
We consider a number of examples of groups together with an infinite conjugation-invariant generating set, including the free group with the generating set of all separable elements, surface groups with the generating set of all non-filling curves, mapping class groups and outer automorphism groups of free groups wit...
Sabine Chu, G. Domat, Christine Gao et al.· Groups, Geometry, and Dynami...· 0 citations
We unify two matching theories, one for finite subsets of groups and the other for finite-dimensional subspaces in a field extension. To achieve this, we study groups equipped with a compatible finitary matroid structure, termed here independence groups. Applying Rado's independent transversal theorem, we derive necess...
Bruhat decompositions give cellular models for split algebraic groups, flag varieties, and maximal compact groups, but motivic boundaries retain orientation and torus-translation data lost in the flag quotient. Over a perfect field of characteristic zero, let the group be connected, split, semisimple, and simply connec...
We study the monodromy action of the mixed braid group $B_{n,\mathcal{P}}$ on the first cohomology of cyclic branched covers of $\mathbb{P}^1$, which are mutually determined by a partition of branch points by equal ramification. The monodromy representation splits into irreducible representations on the $t$-eigenspaces...
V. AthiraE, Pranav Haridas· 0 citations
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