Spaces with local equivalence relations, and their monodromy
The authors study a suggestion of A. Grothendieck [\textit{A. Grothendieck} and \textit{J. L. Verdier}, Lect. Notes Math. 269, 1-217 (1972; Zbl 0249.18021)] regarding invariant sheaves arising from a local equivalance relation on a given space, especially on a foliation. They compare it with the standard model obtained by taking the quotient space of foliations defined by the action of holonomy groupoid. Among other things, they prove that under suitable conditions of connectedness, the above invariant sheaves can be described by the usual monodromy groupoids. As an answer to the realization question, the authors show that every etale topological groupoid arises as the monodromy groupoid of a local equivalence relation on a suitable space \(M\). In an appendix, the authors also provide the topos theoretic aspects of local equivalence relation described above.
scientific article; zbMATH DE number 937156
scientific article