Equivariant pointwise clutching maps

TL;DR

This paper introduces equivariant pointwise clutching maps to facilitate the construction and classification of equivariant vector bundles and Lie group representations over finite sets and surfaces.

Contribution

It defines equivariant pointwise clutching maps and analyzes their topology, aiding in the classification of equivariant vector bundles over two-surfaces.

Findings

Characterization of equivariant pointwise clutching maps

Topological analysis of the set of clutching maps

Application to classifying equivariant vector bundles

Abstract

In the paper, we introduce the terminology equivariant pointwise clutching map. By using this, we give details on how to glue an equivariant vector bundle over a finite set so as to obtain a new Lie group representation such that the quotient map from the bundle to the representation is equivariant. Then, we investigate the topology of the set of all equivariant pointwise clutching maps with respect to an equivariant vector bundle over a finite set. Results of the paper play a key role in classifying equivariant vector bundles over two-surfaces in other papers.