PreprintCC BY 4.0arXiv
On the Nielsen realisation problem for cyclic groups of prime order
Abstract
We solve the Nielsen realisation problem for high-dimensional aspherical manifolds in a new class of special cases. Mainly, we focus on actions of cyclic groups of prime order. A novelty is that it gives topological solutions to the problem with certain high-dimensional fixed point sets, whereas previous solutions of this type were restricted to discrete fixed point sets. This is enabled by recent joint work with Kirstein on isovariant Poincaré duality spaces, and Farrell-Lück-Steimle's obstruction theory to finding approximate fibrations within a homotopy class.
Related
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BibTeX
@misc{kremer2026nielsen,
title = {{On the Nielsen realisation problem for cyclic groups of prime order}},
author = {Christian Kremer},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30620},
eprint = {2608.30620},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30620},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Nielsen realisation problem for cyclic groups of prime order
AU - Christian Kremer
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30620
UR - https://arxiv.org/abs/2608.30620
AB - We solve the Nielsen realisation problem for high-dimensional aspherical manifolds in a new class of special cases. Mainly, we focus on actions of cyclic groups of prime order. A novelty is that it gives topological solutions to the problem with certain high-dimensional fixed point sets, whereas previous solutions of this type were restricted to discrete fixed point sets. This is enabled by recent joint work with Kirstein on isovariant Poincaré duality spaces, and Farrell-Lück-Steimle's obstruction theory to finding approximate fibrations within a homotopy class.
ER -