To send this article to your account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send this article to your Kindle, first ensure firstname.lastname@example.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
For an odd-dimensional oriented hyperbolic manifold with cusps and strongly acyclic coefficient systems, we define the Reidemeister torsion of the Borel–Serre compactification of the manifold using bases of cohomology classes defined via Eisenstein series by the method of Harder. In the main result of this paper we relate this combinatorial torsion to the regularized analytic torsion. Together with results on the asymptotic behaviour of the regularized analytic torsion, established previously, this should have applications to study the growth of torsion in the cohomology of arithmetic groups. Our main result is established via a gluing formula, and here our approach is heavily inspired by a recent paper of Lesch.
In this paper, we define and study strong right-invariant sub-Riemannian structures on the group of diffeomorphisms of a manifold with bounded geometry. We derive the Hamiltonian geodesic equations for such structures, and we provide examples of normal and of abnormal geodesics in that infinite-dimensional context. The momentum formulation gives a sub-Riemannian version of the Euler–Arnol’d equation. Finally, we establish some approximate and exact reachability properties for diffeomorphisms, and we give some consequences for Moser theorems.
We consider the semiclassical Schrödinger equation on a compact negatively curved surface. For any sequence of initial data microlocalized on the unit cotangent bundle, we look at the quantum evolution (below the Ehrenfest time) under small perturbations of the Schrödinger equation, and we prove that, in the semiclassical limit, and for typical perturbations, the solutions become equidistributed on the unit cotangent bundle.
is a compact Kähler manifold. In the present work we propose a construction for weak geodesic rays in the space of Kähler potentials that is tied together with properties of the class
. As an application of our construction, we prove a characterization of
in terms of envelopes.
Classically, an indecomposable class
in the cone of effective curves on a K3 surface
is representable by a smooth rational curve if and only if
. We prove a higher-dimensional generalization conjectured by Hassett and Tschinkel: for a holomorphic symplectic variety
deformation equivalent to a Hilbert scheme of
points on a K3 surface, an extremal curve class
in the Mori cone is the line in a Lagrangian
if and only if certain intersection-theoretic criteria are met. In particular, any such class satisfies
, and the primitive such classes are all contained in a single monodromy orbit.
be a reductive algebraic group over an algebraically closed field of positive characteristic,
the Frobenius kernel of
a maximal torus of
. We show that the parabolically induced
-Verma modules of singular highest weights are all rigid, determine their Loewy length, and describe their Loewy structure using the periodic Kazhdan–Lusztig
-polynomials. We assume that the characteristic of the field is sufficiently large that, in particular, Lusztig’s conjecture for the irreducible