# The Gromov norm of the quaternionic K\"ahler class

## TL;DR

This paper establishes the tightness of the embedding of quaternionic hyperbolic discs into higher-dimensional spaces and calculates the Gromov norm of the quaternionic K"ahler class, advancing understanding of geometric invariants.

## Contribution

It proves the tightness of the embedding of quaternionic hyperbolic discs and determines the Gromov norm of the quaternionic K"ahler class, a previously unknown geometric invariant.

## Key findings

- Embedding of quaternionic hyperbolic disc is tight
- Gromov norm of the quaternionic K"ahler class is explicitly computed
- Advances understanding of quaternionic hyperbolic geometry

## Abstract

We prove that the embedding of the quaternionic hyperbolic disc $H^1_\mathbb{H}$ into quaternionic hyperbolic $n$-space $H^n_\mathbb{H}$ is tight and thereby obtain the value of the Gromov norm of the quaternionic K\"ahler class.