63 papers
This paper utilizes exchange-graph techniques and weighted mixed-angulations to derive explicit presentations of the fundamental groups for genus-zero strata of meromorphic quadratic differentials, generalizing known relations to include higher-order zeroes.
This paper extends Khovanov homology to links in 3-manifolds that are connected sums of orientable interval bundles over surfaces by constructing type D and type A tangle invariants that, when glued along a separating sphere, recover the link's Khovanov homology.
This survey reviews the computation of Weil-Petersson and Masur-Veech volumes for moduli spaces of Riemann surfaces, highlighting their profound impact on combinatorial enumeration, intersection theory, and recursion relations, while drawing parallels between the methods used to calculate these two distinct types of volumes.
This paper characterizes the fundamental group of disjointly tree-graded spaces in terms of the fundamental groups of their constituent pieces, establishing an embedding into an inverse limit of free products even when local simple connectivity is absent.
This paper introduces a reinforcement learning pipeline that successfully simplifies complex knot diagrams and determines the unknotting number of the composite knot $4_1\#9_{10}$ as three, confirming a recently established upper bound.
This paper establishes that outer automorphisms of virtually special groups exhibit either polynomial or exponential growth with algebraic integer stretch factors, constructs a Nielsen-Thurston-like decomposition for coarse-median preserving automorphisms, and proves that their outer automorphism groups satisfy the Tits alternative, are boundary amenable, and have finite virtual cohomological dimension.
This paper establishes a comprehensive -operadic framework for embedding calculus by analyzing towers of truncated right-modules over unital -operads to generalize Goodwillie-Weiss theory to bordism categories, derive new variants for topological and configuration embeddings, and prove key results on convergence, delooping, and homology 4-spheres.
This paper establishes the monotonicity of simplicial volume and dilatation under ribbon concordance for fibered knots, proves the finiteness of their ribbon predecessors, and provides an algorithm to enumerate minimal compressions of surface homeomorphisms to identify strongly homotopy-ribbon concordant knots.
This paper introduces new extensions of Khovanov, Lee, and Bar-Natan homologies for links in that are distinct from previous constructions and yield novel Rasmussen invariants.
The paper proves that for special alternating links where the classical signature provides a sharp lower bound for the unlinking number, this minimum is achieved by crossing changes in any alternating diagram, a result the authors use to determine new unknotting numbers for specific knots with 11 and 12 crossings.
This paper reviews the concept of Kalinin effectivity, establishes that wonderful compactifications of hyperplane arrangements and configuration spaces derived from Kalinin effective manifolds retain this property, and applies these results to demonstrate the effectivity of the Deligne-Mumford space of real rational curves and to investigate Smith-Thom maximality for Hilbert squares.
This paper verifies the AJ conjecture for connected sums of torus knots where and share the same sign, while identifying new cases with repeated factors in the recurrence polynomial that necessitate a slight modification to the conjecture.
This paper demonstrates that quantum cellular automata constitute the degree-zero component of a coarse homology theory, thereby providing a formal framework that explains why the space of such automata forms an Omega-spectrum.
This paper identifies a significant gap in Stanfield's proof of Sachs' conjecture, which asserts that every linklessly embeddable graph admits a linear linkless embedding in .
This paper provides an alternative proof that certain links are not smoothly slice in and explores the implications of this result for detecting exotic smooth structures on .
This paper establishes that a compact polyhedron collapses to a subpolyhedron if and only if it admits a piecewise-linear free deformation retraction onto that subpolyhedron, while also addressing metric characterizations of collapsibility by correcting and providing a counterexample to a claim regarding injective metric spaces.
This paper constructs infinitely many -component Brunnian links of 3-balls in the 4-sphere for each integer by utilizing and providing a new proof for a result concerning splitting spheres for trivial two-component links of 2-spheres.
This paper presents a complete classification of spherical knotoids with up to six crossings and a conjectured complete classification up to seven crossings, utilizing a suite of invariants to distinguish equivalence classes while exploring their symmetries and applications to protein entanglement.
This paper presents explicit infinite families of non-fibered twisted torus knots by demonstrating that the leading coefficients of their Alexander polynomials can assume arbitrary integer values.
This paper introduces loop braid groups as a three-dimensional generalization of classical braid groups to study homeomorphisms of the 3-ball, establishing a connection between Burau matrix representations and the generalized Lefschetz number to derive estimates for the existence and interaction of fixed and periodic points.