A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New stable homotopy refinement of quantum annular Khovanov homology.
problem Quantum topological Hochschild homology and annular Khovanov spectra.
method Introducing quantum topological Hochschild homology (qTHH) and constructing a new stable homotopy refinement of quantum annular Khovanov homology.
result The new stable homotopy refinement agrees with qTHH of spectral Chen-Khovanov tangle bimodules and recovers earlier work.
In this paper we shall establish that properly embedded constant mean curvature one surfaces in H^3 of finite topology are of finite total curvature and each end is regular. In particular, this implies the horosphere is the only simply connected such example, and the catenoid cousins the only annular examples of this n…
A triangulation of a compact 3-manifold is annular-efficient if it is 0-efficient and the only normal, incompressible annuli are thin edge-linking. If a compact 3-manifold has an annular-efficient triangulation, then it is irreducible, boundary-irreducible, and an-annular. Conversely, it is shown that for a compact, ir…
We introduce an sl(n) homology theory for knots and links in the thickened annulus. To do so, we first give a fresh perspective on sutured annular Khovanov homology, showing that its definition follows naturally from trace decategorifications of enhanced sl(2) foams and categorified quantum gl(m), via classical skew Ho…
We prove that the Khovanov-Lee complex of an oriented link, L, in a thickened annulus, A x I, has the structure of a bifiltered complex whose filtered chain homotopy type is an invariant of the isotopy class of L in A x I. Using ideas of Ozsvath-Stipsicz-Szabo as reinterpreted by Livingston, we use this structure to de…
Motivated by topology, we develop a general theory of traces and shadows for an endobicategory, which is a~pair: bicategory C and endobifunctor Σ:C→C. For a graded linear bicategory and a fixed invertible parameter q, we quantize this theory by using the endofunctor Σq such th…
In this article, we study the ramification of the Gauss map of complete minimal surfaces in R^m on annular ends. This work is a continuation of previous work of Dethloff-Ha. We thus give an improvement of the results on annular ends of complete minimal surfaces of Jin-Ru.
Let K be a two-periodic braid and let K be its quotient. In this paper we show there is a spectral sequence from the next-to-top winding number grading of the sutured annular Khovanov homology of the closure of K to the next-to-top winding number grading of the sutured annular Khovanov hom…
In this article, we study the ramification of the Gauss map of complete minimal surfaces in R^3 and R^4 on annular ends. We obtain results which are similar to the ones obtained by Fujimoto and Ru for (the whole) complete minimal surfaces, thus we show that the restriction of the Gauss map to an annular end of such a c…
We use ending laminations for Weil-Petersson geodesics to establish that bounded geometry is equivalent to bounded combinatorics for Weil-Petersson geodesic segments, rays, and lines. Further, a more general notion of non-annular bounded combinatorics, which allows arbitrarily large Dehn-twisting, corresponds to an equ…
In this paper we describe the notion of an annular end of a Riemann surface being of finite type with respect to some harmonic function and prove some theoretical results relating the conformal structure of such an annular end to the level sets of the harmonic function. We then apply these results to understand and cha…
We define a third grading on Khovanov homology, which is an invariant of annular links but changes by ±1 under stabilization. We illustrate the use of our computer implementation, and give some example calculations.
In this article, we study the modified defect relations of the Gauss map of complete minimal surfaces in R3 and R4 on annular ends. We obtain results which are similar to the ones obtained by Fujimoto~[J. Differential Geometry \textbf{29} (1989), 245-262] for (the whole) complete minimal surfaces…
We construct a braid conjugacy class invariant κ by refining Plamenevskaya's transverse element ψ in Khovanov homology via the annular grading. While κ is not an invariant of transverse links, it distinguishes some braids whose closures share the same classical invariants but are not transversely isotopic. Using …
Let L be a link in a thickened annulus. We show that its sutured annular Khovanov homology carries an action of the exterior current algebra of the Lie algebra sl_2. When L is an m-framed n-cable of a knot K in the three-sphere, its sutured annular Khovanov homology carries a commuting action of the symmetric group S_n…
This paper establishes that sutured annular Khovanov homology is not invariant for braid closures under axis-preserving mutations. This follows from an explicit relationship between sutured annular Khovanov homology and the classical Burau representation for braid closures.
The paper evaluates homology for links in a solid torus with special boundary conditions.
problem Evaluating homology for links in a solid torus with specific boundary conditions.
method Using foam evaluation, the paper describes equivariant SL(2) and SL(3) homology for links in the solid torus with a distinguished line.
result Generators of state spaces for annular webs are represented by foams with boundary intersecting a distinguished line, contributing additional terms to the foam evaluation.