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The Thick Part of the PSLn(ℝ)-Hitchin-Riemann Moduli Space has Infinite Volume
Abstract
We prove that the thick part of the PSLn(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.
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BibTeX
@misc{an2026thick,
title = {{The Thick Part of the $\mathrmPSL_n(\mathbbR)$-Hitchin-Riemann Moduli Space has Infinite Volume}},
author = {Huiseong An and Heejae Kim and Mingook Kim and Seungjin Lee and Hongtaek Jung},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.06554},
eprint = {2607.06554},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.06554},
}
RIS
TY - UNPB
TI - The Thick Part of the PSL_n(ℝ)-Hitchin-Riemann Moduli Space has Infinite Volume
AU - Huiseong An
AU - Heejae Kim
AU - Mingook Kim
AU - Seungjin Lee
AU - Hongtaek Jung
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2607.06554
UR - https://arxiv.org/abs/2607.06554
AB - We prove that the thick part of the PSL_n(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.
ER -