标题： 带对合的拓扑群胚和实代数栈 显示英文标题

标题： Topological groupoids with involution and real algebraic stacks

摘要： 对于赋有对合的拓扑群胚，我们关联一个不动点拓扑群胚，推广了具有对合的拓扑空间的不动点子空间。 我们证明，当赋有对合的拓扑群胚来自定义在$\mathbb{R}$上的Deligne-Mumford堆叠时，这个不动点簇与堆叠的实部重合。 这为研究实代数堆叠提供了拓扑框架，特别是实模空间。 最后，我们在这种设定下提出一个类似于Smith-Thom猜想的类型猜想，推广了赋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.