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Analytic Linearization and Holomorphic Extensions of Proper Groupoids

Rui Loja Fernandes, Ning Jiang

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.

Analytic Linearization and Holomorphic Extensions of Proper 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.

Paper Structure

This paper contains 29 sections, 32 theorems, 82 equations.

Table of Contents

  1. Introduction
  2. Analytic 2-metrics
  3. Analytic Riemannian submersions
  4. Transversely invariant analytic metrics
  5. Quasi-actions and analytic metrics
  6. Averaging
  7. Existence of analytic 2-metrics
  8. Analytic linearization of s-proper groupoids
  9. Holomorphic extensions of Lie algebroids
  10. Totally real submanifolds
  11. Definition of holomorphic extension
  12. Existence
  13. Anti-holomorphic involutions
  14. Universal property
  15. Holomorphic extensions of Lie groupoids
  16. ...and 14 more sections

Key Result

Theorem 1

Every s-proper real analytic groupoid admits an analytic linearization around any invariant submanifold.

Theorems & Definitions (64)

  • Theorem 1
  • Corollary 1
  • Theorem 2
  • Corollary 2
  • Corollary 3
  • Theorem 2.1
  • Lemma 2.2
  • proof
  • Lemma 2.3: del2018riemannian
  • Definition 2.4
  • ...and 54 more