标题： 带有对合的拓扑群胚和实代数堆栈 显示英文标题

标题： Topological groupoids with involution and real algebraic stacks

摘要： 对于带有对合的拓扑群胚，我们关联一个固定点的拓扑群胚，推广了带有对合的拓扑空间的固定点子空间。 我们证明当带有对合的拓扑群胚来自于$\mathbb{R}$上的 Deligne-Mumford 模栈时，该固定轨与模栈的实轨重合。 这为研究实代数模栈提供了一个拓扑框架，特别是实模空间。 最后，我们在这种情况下提出了一个类似 Smith-Thom 的猜想，推广了带有对合的拓扑空间的 Smith-Thom 不等式。 显示英文摘要

摘要： To a topological groupoid endowed with an involution, we associate a topological groupoid of fixed points, generalizing the fixed-point subspace of a topological space with involution. We prove that when the topological groupoid with involution arises from a Deligne-Mumford stack over $\mathbb{R}$, this fixed locus coincides with the real locus of the stack. This provides a topological framework to study real algebraic stacks, and in particular real moduli spaces. Finally, we propose a Smith-Thom type conjecture in this setting, generalizing the Smith-Thom inequality for topological spaces endowed with an involution.