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IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-19 DOI: 10.1016/j.aim.2025.110744

Spyridon Kakaroumpas , Zoe Nieraeth

In this work we fully characterize the classes of matrix weights for which multilinear Calderón–Zygmund operators extend to bounded operators on matrix weighted Lebesgue spaces. To this end, we develop the theory of multilinear singular integrals taking values in tensor products of finite dimensional Hilbert spaces. We establish quantitative bounds in terms of multilinear Muckenhoupt matrix weight characteristics and scalar Fujii–Wilson conditions of a tensor product analogue of the convex body sparse operator, of a convex-set valued tensor product analogue of the Hardy–Littlewood maximal operator, and of a multilinear analogue of the Christ–Goldberg maximal operator. These bounds recover the sharpest known bounds in the linear case. Moreover, we define a notion of directional nondegeneracy for multilinear Calderón–Zygmund operators, which is new even in the scalar case. The noncommutativity of matrix multiplication, the absence of duality, and the natural presence of quasinorms in the multilinear setting present several new difficulties in comparison to previous works in the scalar or in the linear case. To overcome them, we use techniques inspired from convex combinatorics and differential geometry.

本文充分刻画了在矩阵加权Lebesgue空间上，多元线性Calderón-Zygmund算子扩展为有界算子的矩阵权的类别。为此，我们发展了在有限维希尔伯特空间张量积中取值的多线性奇异积分理论。我们根据凸体稀疏算子的张量积模拟、Hardy-Littlewood极大算子的凸集值张量积模拟和Christ-Goldberg极大算子的多线性模拟，建立了多线性Muckenhoupt矩阵权特征和标量Fujii-Wilson条件下的定量界。这些边界恢复了线性情况下最尖锐的已知边界。此外，我们定义了多线性Calderón-Zygmund算子的方向非退化的概念，即使在标量情况下也是新的。矩阵乘法的非交换性，对偶性的缺失，以及在多线性情况下拟实的自然存在，与先前在标量或线性情况下的工作相比，提出了几个新的困难。为了克服这些问题，我们使用了受凸组合学和微分几何启发的技术。

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引用次数: 0

On the classification of finite quasi-quantum groups over abelian groups 关于阿贝尔群上有限拟量子群的分类

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-17 DOI: 10.1016/j.aim.2025.110740

Hua-Lin Huang , Gongxiang Liu , Yuping Yang , Yu Ye

Using a variety of methods developed in the theory of finite-dimensional quasi-Hopf algebras, we classify all finite-dimensional coradically graded pointed coquasi-Hopf algebras over abelian groups. As a consequence, we partially confirm the generation conjecture of pointed finite tensor categories due to Etingof, Gelaki, Nikshych and Ostrik.

利用有限维拟hopf代数理论中发展起来的各种方法，对阿贝尔群上的所有有限维根级点拟hopf代数进行了分类。因此，我们部分地证实了Etingof、Gelaki、Nikshych和Ostrik给出的点有限张量范畴的生成猜想。

引用次数: 0

Four-manifolds, two-complexes and the quadratic bias invariant 四流形，二复形和二次偏置不变量

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-17 DOI: 10.1016/j.aim.2025.110728

Ian Hambleton , John Nicholson

Kreck and Schafer produced the first examples of stably diffeomorphic closed smooth 4-manifolds which are not homotopy equivalent. They were constructed by applying the doubling construction to 2-complexes over certain finite abelian groups of odd order. By extending their methods, we formulate a new homotopy invariant on the class of 4-manifolds arising as doubles of 2-complexes with finite fundamental group. As an application we show that, for any

k \geq 2

, there exist a family of k closed smooth 4-manifolds which are all stably diffeomorphic but are pairwise not homotopy equivalent.

Kreck和Schafer首次给出了不同伦等价的稳定微分同构闭光滑4流形的例子。它们是通过对奇阶有限阿贝尔群上的2-复形的加倍构造而得到的。通过推广它们的方法，我们在有限基群的2-复形的对偶产生的4-流形上，构造了一个新的同伦不变量。作为一个应用，我们证明了对于任意k≥2，存在k个闭光滑4流形族，它们都是稳定微分同构的，但对不同伦等价。

引用次数: 0

A Serrin-type over-determined problem for Hessian equations in the exterior domain 外域Hessian方程的serrin型超定问题

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-16 DOI: 10.1016/j.aim.2025.110737

Bo Wang , Zhizhang Wang

In this paper, we consider the Hessian equations in some exterior domain with prescribed asymptotic behavior at infinity and Dirichlet-Neumann conditions on its interior boundary. We obtain that there exists a unique bounded domain such that the over-determined problem admits a unique strictly convex solution.

本文考虑了外域上具有无穷远渐近特性的Hessian方程及其内边界上的Dirichlet-Neumann条件。得到了存在唯一有界区域，使得超定问题有唯一严格凸解。

引用次数: 0

Short hierarchically hyperbolic groups II: Quotients and the Hopf property for Artin groups 短层次双曲群II: Artin群的商和Hopf性质

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-16 DOI: 10.1016/j.aim.2025.110736

Giorgio Mangioni, Alessandro Sisto

We prove that most Artin groups of large and hyperbolic type are Hopfian, meaning that every self-epimorphism is an isomorphism. The class covered by our result is generic, in the sense of Goldsborough-Vaskou. Moreover, assuming the residual finiteness of certain hyperbolic groups with an explicit presentation, we get that all large and hyperbolic type Artin groups are residually finite. We also show that “most” quotients of the five-holed sphere mapping class group are hierarchically hyperbolic, up to taking powers of the normal generators of the kernels.

The main tool we use to prove both results is a Dehn-filling-like procedure for short hierarchically hyperbolic groups (these also include e.g. non-geometric 3-manifolds, and triangle- and square-free RAAGs).

我们证明了大多数的大双曲型Artin群是Hopfian的，这意味着每一个自外同构都是一个同构。在Goldsborough-Vaskou的意义上，我们的结果所涵盖的类是泛型的。在此基础上，给出了双曲型群的剩余有限性，得到了所有大的双曲型Artin群都是剩余有限的。我们还证明了五孔球映射类群的“大多数”商在层次上是双曲的，直到取核的正规生成器的幂。我们用来证明这两个结果的主要工具是一个类似dehn填充的过程，用于短的层次双曲群（这些也包括例如非几何3流形，以及无三角形和无平方的RAAGs）。

引用次数: 0

Boundary value problems in graph Lipschitz domains in the plane with A∞-measures on the boundary 边界上有A∞测度的平面图Lipschitz域的边值问题

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-16 DOI: 10.1016/j.aim.2025.110734

Fernando Ballesta-Yagüe, María J. Carro

We prove several results for the Dirichlet, Neumann and Regularity problems for the Laplace equation in graph Lipschitz domains in the plane, considering

A_{\infty}

-measures on the boundary. More specifically, we study the

L^{p, 1}

-solvability for the Dirichlet problem, complementing results of [25] and [10]. Then, we study

L^{p}

-solvability of the Neumann problem, obtaining a range of solvability which is empty in some cases, a clear difference with the arc-length case. When it is not empty, it is an interval, and we consider solvability at its endpoints, establishing conditions for Lorentz space solvability when

p > 1

and atomic Hardy space solvability when

p = 1

. Solving the Lorentz endpoint leads us to a two-weight Sawyer-type inequality, for which we give a sufficient condition. Finally, we show how to adapt to the Regularity problem the results for the Neumann problem.

我们证明了平面上考虑边界上A∞测度的图Lipschitz域上拉普拉斯方程的Dirichlet、Neumann和正则性问题的几个结果。更具体地说，我们研究了Dirichlet问题的Lp，1可解性，补充了[25]和[10]的结果。然后，我们研究了Neumann问题的lp可解性，得到了在某些情况下是空的可解范围，这与弧长情况有明显的区别。当它不为空时，它是一个区间，考虑其端点处的可解性，建立了p=1时洛伦兹空间可解和p=1时原子Hardy空间可解的条件。求解洛伦兹端点可得到一个二权索耶型不等式，并给出了该不等式的充分条件。最后，我们展示了如何将正则性问题的结果应用于诺伊曼问题。

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引用次数: 0

The K-theory of the C*-algebras associated to rational functions 与有理函数相关的C*代数的k理论

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-16 DOI: 10.1016/j.aim.2025.110738

Jeremy B. Hume

We compute the K-theory of the three

C^{⁎}

-algebras associated to a rational function R acting on the Riemann sphere, its Fatou set, and its Julia set. The latter

C^{⁎}

-algebra is a unital UCT Kirchberg algebra and is thus classified by its K-theory. The K-theory in all three cases is shown to depend only on the degree of R, the critical points of R, and the Fatou cycles of R. Our results yield new dynamical invariants for rational functions and a

C^{⁎}

-algebraic interpretation of the Density of Hyperbolicity Conjecture for quadratic polynomials. These calculations are possible due to new exact sequences in K-theory we induce from morphisms of

C^{⁎}

-correspondences.

我们计算了作用于Riemann球上的一个有理函数R及其Fatou集和Julia集的三个C -代数的k理论。后一种C -代数是一个统一的UCT Kirchberg代数，因此可以用它的k理论来分类。这三种情况下的k理论只依赖于R的度、R的临界点和R的Fatou环。我们的结果给出了有理函数的新的动态不变量和二次多项式的双曲猜想密度的C - C -代数解释。这些计算是可能的，因为我们从C -对应的态射中推导出了k理论中的新的精确序列。

引用次数: 0

A quantum trace map for 3-manifolds 3流形的量子轨迹映射

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-16 DOI: 10.1016/j.aim.2025.110735

Stavros Garoufalidis , Tao Yu

We define a quantum trace map from the skein module of a 3-manifold with torus boundary components to a module (left and right quotient of a quantum torus) constructed from an ideal triangulation. Our map is a 3-dimensional version of the well-known quantum trace map on surfaces introduced by Bonahon and Wong and further developed by Lê.

我们定义了从具有环面边界分量的3流形的串模到由理想三角剖分构造的模（量子环面的左商和右商）的量子迹映射。我们的地图是Bonahon和Wong提出的著名的表面量子迹图的三维版本，并由Lê进一步发展。

引用次数: 0

A∞ deformations of extended Khovanov arc algebras and Stroppel's conjecture 扩展Khovanov弧代数的A∞变形与Stroppel猜想

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-11 DOI: 10.1016/j.aim.2025.110733

Severin Barmeier , Zhengfang Wang

Extended Khovanov arc algebras

K_{m}^{n}

are graded associative algebras which naturally appear in a variety of contexts, from knot and link homology, low-dimensional topology and topological quantum field theory to representation theory and symplectic geometry. C. Stroppel conjectured in her ICM 2010 address that the bigraded Hochschild cohomology groups of

K_{m}^{n}

vanish in a certain range, implying that the algebras

K_{m}^{n}

admit no nontrivial A_∞ deformations, in particular that the algebras are intrinsically formal.

Whereas Stroppel's conjecture is known to hold for the algebras

K_{m}^{1}

and

K_{1}^{n}

by work of Seidel and Thomas, we show that

K_{m}^{n}

does in fact admit nontrivial A_∞ deformations with nonvanishing higher products for all

m, n \geq 2

We describe both the extended Khovanov arc algebras

K_{m}^{n}

and their Koszul duals concretely as path algebras of quivers with relations. This allows us to give an explicit algebraic construction of A_∞ deformations of

K_{m}^{n}

by using the correspondence between A_∞ deformations of a Koszul algebra and filtered associative deformations of its Koszul dual.

扩展Khovanov弧代数Kmn是一种自然出现在各种背景下的梯度结合代数，从结和链接同调，低维拓扑和拓扑量子场论到表示理论和辛几何。C. Stroppel在ICM 2010的演讲中推测Kmn的梯度Hochschild上同群在一定范围内消失，这意味着代数Kmn不允许非平凡a∞变形，特别是代数本质上是形式的。然而，通过Seidel和Thomas的工作，已知对于代数Km1和K1n， Stroppel猜想是成立的，我们证明Kmn实际上承认非平凡的A∞变形，并且对于所有m，n≥2，具有不消失的高积。我们将扩展Khovanov弧代数Kmn及其kozul对偶具体描述为带关系的颤振的路径代数。这允许我们利用kozul代数的A∞变形与其kozul对偶的过滤关联变形之间的对应关系，给出Kmn的A∞变形的显式代数构造。

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引用次数: 0

Hirzebruch-Riemann-Roch for global matrix factorizations 全局矩阵分解的Hirzebruch-Riemann-Roch

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-12-11 DOI: 10.1016/j.aim.2023.109076

Bumsig Kim

We prove a Hirzebruch-Riemann-Roch type formula for global matrix factorizations. This is established by an explicit realization of the abstract Hirzebruch-Riemann-Roch type formula of Shklyarov. We also show a Grothendieck-Riemann-Roch type theorem.

证明了一个全局矩阵分解的Hirzebruch-Riemann-Roch型公式。这是通过对Shklyarov的抽象Hirzebruch-Riemann-Roch型公式的显式实现来建立的。我们还证明了一个Grothendieck-Riemann-Roch型定理。

引用次数: 0

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