Involutions on surfaces

TL;DR

This paper provides a comprehensive classification of all involutions on closed surfaces using modern equivariant surgery techniques, resolving longstanding classical questions in the field.

Contribution

It offers a complete, modern classification of involutions on closed surfaces, filling gaps in historical understanding with new methods.

Findings

Complete classification of involutions on closed surfaces

Application of equivariant surgery techniques

Resolution of classical open questions

Abstract

We use equivariant surgery to classify all involutions on closed surfaces, up to isomorphism. Work on this problem is classical, dating back to the nineteenth century, but some questions seem to have been left unanswered. We give a modern treatment that leads to a complete classification.