63 papers
The paper proves that transitive Anosov flows are abundant on fibered hyperbolic 3-manifolds by demonstrating that a finite index subgroup of the mapping class group consists of elements whose mapping tori carry such flows, thereby establishing that these manifolds have positive density within the set of all fibered hyperbolic 3-manifolds.
This paper demonstrates that in the general framework of -boundaries, the boundary of an infinitely ended group admitting a splitting over finite subgroups is canonically homeomorphic to the dense amalgam of the limit sets of its factor subgroups.
This paper disproves a homological generalization of the generalized Property R conjecture by demonstrating the existence of 2-component framed links in that surger to a connected sum of homology manifolds yet are not handleslide equivalent to a split link.
This paper introduces a refined combinatorial 1-cocycle with Laurent polynomial coefficients to define refined tangle equations, providing a quantitative method to analyze knot isotopies and distinguish knot diagrams based on the solvability of these equations.
The paper demonstrates that the 2-component unlink in the 4-sphere admits infinitely many distinct isotopy classes of spanning 3-disks that are Brunnian.
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 necessary and sufficient cohomological conditions for representing classes by Real embedded surfaces in 4-manifolds and derives two versions of an adjunction inequality for their genus when Real Seiberg-Witten invariants are non-zero, demonstrating that the minimal genus for Real surfaces can exceed that of arbitrary embedded surfaces.
This paper proves that the flip map involution on Khovanov homology is determined by its behavior on unlinks and acts as the identity over , thereby confirming a conjecture on the Viro flip map and establishing the equivalence of induced involutions for strongly invertible knots.
This paper constructs a braided balanced category of half-braided algebras and bimodules internal to a braided category to interpret stated skeins as a TQFT, specifically relating this construction to the Kerler-Lyubashenko TQFT in the case of finite-dimensional ribbon factorizable Hopf algebras.
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 generalizes the classical Morlet-Burghelea-Lashof-Kirby-Siebenmann smoothing theory delooping of disc diffeomorphism groups to various disc embedding spaces, establishing their equivalence to specific loop spaces of quotient classifying spaces and demonstrating how these deloopings unify Hatcher and Budney group actions into a framed little discs operad action.
This paper constructs analogs of Khovanov-Jacobsson classes and the Rasmussen invariant for links in the boundary of smooth oriented 4-manifolds by utilizing skein lasagna modules derived from equivariant and deformed link homology, while establishing non-vanishing results, decomposition theorems, and conditions for extending functoriality to immersed cobordisms.
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 proposes and rigorously establishes a symmetrization relation between 4d BPS quivers and 3d symmetric quivers, demonstrating that the wall-crossing structure of 4d Argyres-Douglas theories is isomorphic to the unlinking of their 3d counterparts and that these symmetric quivers successfully capture the Schur indices of the original 4d theories.
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 extends Masur and Minsky's result on the quasi-isometry between Teichmüller space and the curve graph to the -multicurve graph by electrifying the space along regions of small extremal length for curves, utilizing a new distance bound derived from intersection numbers.
The paper establishes that the number of compact, essential, orientable, non-isotopic surfaces with a fixed Euler characteristic embedded in a finite-volume hyperbolic 3-manifold is bounded by a polynomial function of the manifold's volume, where the degree of the polynomial depends linearly on the absolute value of the Euler characteristic.
This paper extends the complete census of orientable cusped hyperbolic 3-manifolds to 10 tetrahedra, identifying 150,730 new manifolds and their triangulations to determine 439,898 exceptional Dehn fillings, discover 1,849 new simplest hyperbolic knot exteriors, and provide the first example of such a manifold containing a closed totally geodesic surface.
This paper provides a geometric interpretation of virtual knotoids as arcs in thickened surfaces, demonstrating that virtual knotoid theory generalizes classical knotoid theory and thereby proving a conjecture by Kauffman and the first author.
This paper investigates the property for mapping class groups of infinite-type surfaces, establishing conditions under which any finite set of non-trivial elements can be simultaneously combined with a single infinite-order element to generate a free product structure.