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Hamiltonian actions on 0-shifted cosymplectic groupoids

Daniel López Garcia, Fabricio Valencia

Abstract

We introduce the notion of 0-shifted cosymplectic structure on differentiable stacks and develop a corresponding moment map theory for Hamiltonian cosymplectic actions. We present a reduction procedure, establish a version of the Kirwan convexity theorem, and obtain examples of Morse-Bott Lie groupoid morphisms.

Hamiltonian actions on 0-shifted cosymplectic groupoids

Abstract

We introduce the notion of 0-shifted cosymplectic structure on differentiable stacks and develop a corresponding moment map theory for Hamiltonian cosymplectic actions. We present a reduction procedure, establish a version of the Kirwan convexity theorem, and obtain examples of Morse-Bott Lie groupoid morphisms.

Paper Structure

This paper contains 4 sections, 7 theorems, 16 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Precosymplectic Hamiltonian actions
  3. 0-shifted cosymplectic structures
  4. Moment map morphisms

Key Result

Lemma 2.1

If $(M,\omega,\eta)$ is a precosymplectic manifold then $\ker(\flat)=\ker(\omega)\cap \ker(\eta)$.

Figures (1)

  • Figure 1: $\mu(X_0)$ for $S=\mathbb{C}^3$ and $\mathfrak{n}=\langle \xi_1 \rangle$.

Theorems & Definitions (17)

  • Lemma 2.1
  • proof
  • Definition 2.2
  • Example 2.3
  • Example 2.4
  • Proposition 2.5
  • Example 2.6
  • Definition 3.1
  • Proposition 3.2
  • proof
  • ...and 7 more