The Thick Part of the $\mathrm{PSL}_n(\mathbb{R})$-Hitchin-Riemann Moduli Space has Infinite Volume
Year: 2026
Type: preprint
Abstract: We prove that the thick part of the $\mathrm{PSL}_n(\mathbb{R})$-Hitchin-Riemann moduli space has infinite total Atiyah--Bott--Goldman volume for $n>2$. This result stands in contrast to Mumford's compactness criterion. To achieve this result, we employ Goldman flows and internal sequences to find an infinite series of subsets of identical volume, the images of which in the Hitchin-Riemann moduli space are all mutually disjoint and sit in the thick part.
Source: arXiv (Cornell University)
Institutions: Yonsei University, Sungkyunkwan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167694412