72 papers
This paper establishes that the number of quasi-Fuchsian surface subgroups in finite-volume noncompact hyperbolic 3-manifolds grows asymptotically as , a result that implies a similar lower bound for purely pseudo-Anosov surface subgroups in mapping class groups, while also demonstrating the existence of infinitely many conjugacy classes of surface subgroups with accidental parabolics.
This paper establishes homological stability for automorphisms of symmetric bilinear forms over a broad class of principal ideal domains, thereby determining a significant portion of the stable cohomology of odd orthogonal groups over the integers in low degrees.
This paper proves that every locally compact strongly topological gyrogroup possesses a suitable set, thereby affirmatively resolving a question previously posed by F. Lin and colleagues.
This paper establishes that central extensions of certain separable hyperbolic and double coset separable groups inherit product and double coset separability properties, provided they are subgroup separable, and demonstrates that double coset separability is preserved under direct products with finitely generated nilpotent groups.
This paper introduces the concept of "zippers" as a novel and streamlined method for constructing universal circles—key dynamical structures associated with hyperbolic 3-manifolds—by deriving them directly from uniform quasimorphisms or uniform left orders.
This paper introduces a unified definition of Anosov representations for relatively hyperbolic groups that encompasses various existing notions of geometrically finite behavior and proves their stability under deformations satisfying specific dynamical conditions on peripheral subgroups.
This paper demonstrates that co-Hopfianity is not a profinite property by constructing two finitely generated residually finite groups with isomorphic profinite completions, where one is co-Hopfian and the other is not, utilizing Wise's Rips construction and a specific preimage subgroup technique.
This paper establishes the compactness of a character variety classifying continuous group actions on algebraic real hyperbolic spaces of arbitrary dimension, unifying previous compactifications and proving rigidity results for irreducible representations via the introduction of algebraic and abstract cross-ratios.
This paper introduces a class of algebras derived from labeled directed graphs, establishes their properties as axial algebras with specific fusion laws and simplicity, and demonstrates that any group can be realized as the automorphism group of infinitely many such simple algebras.
This paper constructs canonical sets of right coset representatives for the congruence subgroups , , and to prove that their corresponding fundamental domains are connected, utilizing a study of the projective line and a multiplicity function that is shown to be one less than a more computable function .
This paper refines classical embedding theorems by proving that recursively presented groups admit quasi-isometric malnormal embeddings into finitely presented groups with the congruence extension property and controlled decidability, while also establishing that any countable group can be malnormally embedded into a finitely presented group with a prescribed word length function.
The 21st edition of the Kourovka Notebook is a comprehensive collection of open problems in group theory, featuring 150 new challenges and updates on previous issues proposed by mathematicians worldwide since its inception in 1965.