A unified calculation for Gromov norm of K\"ahler class of bounded symmetric domains

TL;DR

This paper introduces a simplified, unified method to compute the Gromov norm of the K"ahler class for all bounded symmetric domains, extending previous specific cases and utilizing the Polydisc Theorem.

Contribution

It provides a unified, simplified calculation approach for the Gromov norm of the K"ahler class across all bounded symmetric domains, building on prior work.

Findings

Unified calculation method for Gromov norm

Equality condition for ideal triangles on Shilov boundary

Simplification achieved through combined ideas and Polydisc Theorem

Abstract

We provide a unified way to calculate the Gromov norm of the K\"ahler class of all (compact manifolds uniformized by) bounded symmetric domains. This was done for three classical domains by Domin and Toledo and for the general case by Clerc and \O rsted. Here, the calculation is much simplified by a combination of the ideas in Domin-Toledo and a work of Toledo, with the help of the Polydisc Theorem. The equality is achieved if and only if the triangle is ideal with three vertices on the Shilov boundary.