Categories of orbit types for proper Lie groupoids

TL;DR

This paper introduces a new categorical framework for classifying orbit types in proper Lie groupoids, aiming to better understand the complex structure of quotient spaces arising from group actions.

Contribution

It proposes a novel database category of orbit types for proper Lie groupoids, connecting geometric quantization and groupoid theory.

Findings

Defines a database category capturing orbit type information

Links orbit types to geometric quantization concepts

Provides a structured approach to analyze quotient space complexity

Abstract

It is widely understood that the quotient space of a topological group action can have a complicated combinatorial structure, indexed somehow by the sotropy groups of the action, but how best to record this structure seems unclear. This sketch defines a database category of orbit types for a proper Lie groupoid (based on recent work with roots in the theory of geometric quantization) as an attempt to capture some of this information.