Integration of Singular Foliations via Paths

Abstract We give a new construction of the holonomy and fundamental groupoids singular foliation. In contrast with existing Androulidakis Skandalis, our method proceeds by taking quotient an infinite-dimensional space paths. This strategy is direct extension classical for regular foliations mirrors integration Lie algebroids via paths (per Crainic Fernandes). this way, we obtain characterization foliation that more clearly reflects homotopic character these invariants. As application work, prove constructions groupoid have functorial properties.