On the Topology of Real Bundle Pairs over Nodal Symmetric Surfaces

TL;DR

This paper classifies real bundle pairs over symmetric surfaces, including nodal cases, and analyzes automorphisms, providing a comprehensive understanding of their isomorphism classes up to deformation.

Contribution

It offers an alternative proof for classifying real bundle pairs over smooth symmetric surfaces and extends this classification to nodal symmetric surfaces, also classifying automorphisms.

Findings

Classification of real bundle pairs over smooth symmetric surfaces

Extension of classification to nodal symmetric surfaces

Homotopy classes of automorphisms characterized

Abstract

We give an alternative argument for the classification of real bundle pairs over smooth symmetric surfaces and extend this classification to nodal symmetric surfaces. We also classify the homotopy classes of automorphisms of real bundle pairs over symmetric surfaces. The two statements together describe the isomorphisms between real bundle pairs over symmetric surfaces up to deformation.