Year: 2022
Type: preprint
Abstract: We show that the natural conjugation invariant cone structure on the linear symplectic group $\mathrm{Sp}(2n)$ is globally hyperbolic in the positively elliptic region $\mathrm{Sp}_{\mathrm{ell}}^{+}(2n)$. This answers a question by Abbondandolo, Benedetti and Polterovich and shows a formula for a bi-invariant Lorentzian distance function dened by these authors for elements in this region. Moreover we give a characterisation of the positively elliptic region and of $-id \in\mathrm{Sp}(2n)$ in terms of the causality of this cone structure.
Source: arXiv (Cornell University)
Author: Hedicke, Jakob
Institutions: Centre de recherches mathématiques, Université de Montréal
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4308618935