Morphisms between spaces of leaves viewed as fractions
Jean Pradines
TL;DR
This paper revisits a 1989 work on morphisms between leaf spaces, discussing their relation to calculus of fractions and generalized morphisms in Lie groupoids, with added commentary on subsequent related research.
Contribution
It provides a detailed comparison of Gabriel-Zisman calculus of fractions and Haefliger-Skandalis-Hilsum generalized morphisms in the context of Lie groupoids.
Findings
Clarifies the relationship between different approaches to inverting equivalences.
Includes updated comments on related literature and methods.
Enhances understanding of morphisms between leaf spaces in differential geometry.
Abstract
Reprint of a 1989 paper including minor corrections of misprints. Added comments (11 pages) about later related papers in the literature concerning comparison of Gabriel-Zisman calculus of (right) fractions and the use of generalized morphims in the sense of Haefliger-Skandalis-Hilsum for inverting differentiable equivalences between Lie groupoids.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models