I apologize if this question is not appropriate for this site. I am aware of the n'th Haefliger groupoid, which acts as a classifying space for codimension-n foliations. Is there something similar for singular foliations, with varying codimension? Furthermore, does this object admit a nice construction in terms of the Haefliger groupoids?
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$\begingroup$ In a now-deleted answer, Gael Meigniez asks: "Are your foliations Riemannian?" $\endgroup$– S. Carnahan ♦Commented Feb 20, 2017 at 14:52
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$\begingroup$ Thank you for clarifying that; they are not Riemannian foliations. $\endgroup$– MathemologistCommented Feb 20, 2017 at 14:55
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