Browsing by Author "Stern, Mark"
Now showing items 1-6 of 6
-
Harmonic Forms, Price Inequalities, and Benjamini-Schramm Convergence
We study Betti numbers of sequences of Riemannian manifolds which Benjamini-Schramm converge to their universal covers. Using the Price inequalities we developed elsewhere, we derive two distinct convergence results. First, ... -
Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem
(Journal of Differential Geometry, 2019-12-06)We study finite action anti-self-dual Yang-Mills connections on the multi-Taub-NUT space. We establish the curvature and the harmonic spinors decay rates and compute the index of the associated Dirac operator. This is ... -
Instantons on multi-Taub-NUT Spaces II: Bow Construction
Unitary anti-self-dual connections on Asymptotically Locally Flat (ALF) hyperk\"ahler spaces are constructed in terms of data organized in a bow. Bows generalize quivers, and the relevant bow gives rise to the underlying ... -
Nonlinear Harmonic Forms and an Indefinite Bochner Formula
(2017-06-01)We introduce the study of nonlinear harmonic forms. These are forms which minimize the $L_2$ energy in a cohomology class subject to a nonlinear constraint. In this note, we include only motivations and the most basic existence ... -
On the Betti Numbers of Finite Volume Hyperbolic Manifolds
We obtain strong upper bounds for the Betti numbers of compact complex-hyperbolic manifolds. We use the unitary holonomy to improve the results given by the most direct application of the techniques of [DS17]. We also provide ... -
Price Inequalities and Betti Number Growth on Manifolds without Conjugate Points
(2017-06-01)We derive Price inequalities for harmonic forms on manifolds without conjugate points and with a negative Ricci upper bound. The techniques employed in the proof work particularly well for manifolds of non-positive sectional ...
