Analytic Linearization and Holomorphic Extensions of Proper Groupoids

TL;DR

This paper proves that s-proper analytic groupoids can be analytically linearized around invariant submanifolds and extended holomorphically, advancing the understanding of their local and complex structures.

Contribution

It introduces a method for analytic linearization of s-proper analytic groupoids and demonstrates their holomorphic extension, a novel result in the study of groupoid structures.

Findings

Analytic linearization around invariant submanifolds achieved.

Existence of holomorphic extensions for s-proper analytic groupoids established.

Enhanced understanding of local and complex structures of groupoids.

Abstract

We establish analytic linearization of s-proper analytic groupoids around invariant submanifolds. We apply this result to show that any such groupoid admits a holomorphic extension.