This expository paper recounts the development and application of the concept of a diffeological groupoid, from its introduction in 1985 to its use in current research. We demonstrate how this single concept has served as a powerful and unifying tool for defining fundamental structures, analyzing the stratification of complex spaces like orbifolds, building a bridge to noncommutative geometry, and, most recently, forging new approaches to geometric quantization. The paper aims to provide a cohesive narrative of this journey, making explicit certain concepts like the "Klein groupoid" and showcasing the enduring vitality of the diffeological groupoid in modern geometry and physics.
Citation: Patrick Iglesias-zemmour. Groupoids in diffeology[J]. Electronic Research Archive, 2025, 33(12): 7957-7973. doi: 10.3934/era.2025350
This expository paper recounts the development and application of the concept of a diffeological groupoid, from its introduction in 1985 to its use in current research. We demonstrate how this single concept has served as a powerful and unifying tool for defining fundamental structures, analyzing the stratification of complex spaces like orbifolds, building a bridge to noncommutative geometry, and, most recently, forging new approaches to geometric quantization. The paper aims to provide a cohesive narrative of this journey, making explicit certain concepts like the "Klein groupoid" and showcasing the enduring vitality of the diffeological groupoid in modern geometry and physics.
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Patrick Iglesias-zemmour. Groupoids in diffeology[J]. Electronic Research Archive, 2025, 33(12): 7957-7973. doi: 10.3934/era.2025350
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