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Perverse schobers, stability conditions and quadratic differentials I
Merlin Christ, Fabian Haiden, Yu Qiu
We develop a unified approach for identifying spaces of stability conditions of triangulated categories arising from weighted marked surfaces with moduli spaces of quadratic differ…
Categorical Lusztig cycles and weave schobers
Roger Casals, Merlin Christ
We establish the foundations of categorical weave calculus, developing the diagrammatic calculus of weaves and braid varieties within the study of Calabi-Yau triangulated categorie…
-categorical group quotients via skew group algebras
Merlin Christ
We relate group quotients of dg-categories and linear stable -categories. Given a group acting on a dg-algebra, we prove that the skew group dg-algebra is Morita equivalent…
Perverse schobers, stability conditions and quadratic differentials II: relative graded Brauer graph algebras
Merlin Christ, Fabian Haiden, Yu Qiu
We introduce a class of dg-algebras which generalize the classical Brauer graph algebras. They are constructed from mixed-angulations of surfaces and often admit a (relative) Calab…
Induction in perverse schobers and cluster tilting theory
Merlin Christ
We exhibit gluing properties of cluster tilting subcategories in exact -categories within the framework of perverse schobers on surfaces with boundary. These results are ba…
Cluster theory of topological Fukaya categories. Part II: Higher Teichmüller theory
Merlin Christ
We construct relative -Calabi--Yau categories related with higher Teichmüller theory. We further study their corresponding cosingularity categories and the additive categorific…