Conjecture on bounded holonomy and compact regular holonomy

Let F\cal F be a Riemannian foliation with bounded holonomy, and suppose that no leaf has infinite fundamental group. Let HpH_p denote the holonomy group at pp. Bounded-holonomy conjecture. The group HpH_p is compact and the holonomy is regular. This is presented as a possible relation between bounded holonomy, compactness, and regularity; the supplied text gives no resolution.

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Primary source

Llohann D. Sperança, “On Riemannian Foliations over Positively Curved Manifolds”, arXiv:1602.01046 (2016).

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