Cyclic Nielsen realization for del Pezzo surfaces

Seraphina Eun Bi Lee; Tudur Lewis; Sidhanth Raman

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arXiv · 2504.17235

Cyclic Nielsen realization for del Pezzo surfaces

Seraphina Eun Bi Lee·Tudur Lewis·Sidhanth Raman

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Abstract

The cyclic Nielsen realization problem for a closed, oriented manifold asks whether any mapping class of finite order can be represented by a homeomorphism of the same order. In this article, we resolve the smooth, metric, and complex cyclic Nielsen realization problem for certain "irreducible" mapping classes on the family of smooth 4-manifolds underlying del Pezzo surfaces. Both positive and negative examples of realizability are provided in various settings. Our techniques are varied, synthesizing results from reflection group theory and 4-manifold topology.

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Seraphina Eun Bi Lee, Tudur Lewis, Sidhanth Raman. 2025-04-24. Cyclic Nielsen realization for del Pezzo surfaces. https://arxiv.org/abs/2504.17235

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