Nonsmoothable group actions on elliptic surfaces

TL;DR

This paper demonstrates that for certain elliptic surfaces, there exist cyclic group actions that are locally linear but cannot be smoothed for infinitely many smooth structures, extending previous results.

Contribution

It establishes the existence of nonsmoothable cyclic group actions on elliptic surfaces under specific conditions, broadening understanding of group actions in differential topology.

Findings

Existence of nonsmoothable G-actions on elliptic surfaces for certain n

Extension of previous results to more general conditions

Infinitely many smooth structures admit nonsmoothable actions

Abstract

Let G be a cyclic group of order 3, 5 or 7, and X=E(n) be the relatively minimal elliptic surface with rational base. In this paper, we prove that under certain conditions on n, there exists a locally linear G-action on X which is nonsmoothable with respect to infinitely many smooth structures on X. This extends the main result of our previous paper.