The Dehn function of Sp(2n;Z)

TL;DR

This paper proves that the lattice Sp(2p;Z) has quadratic Dehn function for p at least 5, providing insights into geometric group theory and implications for the distortion of the Torelli group.

Contribution

It establishes the quadratic Dehn function for Sp(2p;Z) when p ≥ 5, advancing understanding of lattice geometry and related group distortions.

Findings

Sp(2p;Z) has quadratic Dehn function for p ≥ 5

Implication that Torelli group in large genus is at most exponentially distorted

Supports Gromov's conjecture for certain lattices

Abstract

Gromov conjectured that any irreducible lattice in a symmetric space of rank at least 3 should have at most polynomial Dehn function. We prove that the lattice Sp(2p;Z) has quadratic Dehn function when p is at least 5. By results of Broaddus, Farb, and Putman, this implies that the Torelli group in large genus is at most exponentially distorted.