Bulletin of the London Mathematical Society最新文献

Let $��X�\subset �P^{�n�+�1�}�$ be a smooth Fano hypersurface of dimension $�n$ and degree $�d$. The derived category of coherent sheaves on $�X$ contains an interesting subcategory called the Kuznetsov component $�A_X$. We show that this subcategory, together with a certain autoequivalence called the rotation functor, determines $�X$ uniquely if $��d�>�3�$ or if $��d�=�3�$ and $��n�>�3�$. This generalizes a result by Huybrechts and Rennemo, who proved the same statement under the additional assumption that $�d$ divides $��n�+�2�$.

We investigate finite groups with the Magnus Property (MP), where a group is said to have the MP if whenever two elements have the same normal closure, then they are conjugate or inverse conjugate. In particular, we observe that a finite MP group is solvable, determine the finite primitive MP groups, and determine all the possible orders of the chief factors of a finite MP group. We also determine the MP finite direct products of finite primitive groups, as well as the MP crown-based powers of a finite monolithic primitive group.

The signature of a rectifiable path is a tensor series in the tensor algebra whose coefficients are definite iterated integrals of the path. The signature characterizes the path up to a generalized form of reparameterization. It is a classical result of Chen that the log-signature (the logarithm of the signature) is a Lie series. A Lie series is polynomial if it has finite degree. We show that the log-signature is polynomial if and only if the path is a straight line up to reparameterization. Consequently, the log-signature of a rectifiable path either has degree one or infinite support. Though our result pertains to rectifiable paths, the proof uses rough path theory, in particular that the signature characterizes a rough path up to reparameterization.

The set of equivalence classes of cobounded actions of a group $�G$ on different hyperbolic metric spaces carries a natural partial order. Following Abbott–Balasubramanya–Osin, the group $�G$ is $�H$-accessible if the resulting poset has a largest element. In this paper, we prove that every nongeometric 3-manifold has a finite cover with $�H$-inaccessible fundamental group and give conditions under which the fundamental group of the original manifold is $�H$-inaccessible. We also prove that every Croke–Kleiner admissible group (a class of graphs of groups that generalizes fundamental groups of three-dimensional graph manifolds) has a finite index subgroup that is $�H$-inaccessible.

The spectrum of the Dirichlet Laplacian on any quasi-conical open set coincides with the non-negative semi-axis. We show that there is a connected quasi-conical open set such that the respective Dirichlet Laplacian has a positive (embedded) eigenvalue. This open set is constructed as the tower of cubes of growing size connected by windows of vanishing size. Moreover, we show that the sizes of the windows in this construction can be chosen so that the absolutely continuous spectrum of the Dirichlet Laplacian is empty.

We show that in a Morse local-to-global group where stable subgroups are separable, the product of any stable subgroups is separable. As an application, we show that the product of stable subgroups in virtually special groups is separable.

Let $��X�,�Y�$ be two Banach spaces, $��F�:�X�\to �Y�$ be an $�\epsilon$-norm-additive map for some $��\epsilon �⩾�0�$, that is,