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We introduce Fenchel-Nielsen coordinates on Teicm\"uller spaces of surfacesof infinite type. The definition is relative to a given pair of pantsdecomposition of the surface. We start by establishing conditions under whichany pair of pants decomposition on a hyperbolic surface of infinite type can beturned into a geometric decomposition, that is, a decomposition into hyperbolicpairs of pants. This is expressed in terms of a condition we introduce andwhich we call Nielsen convexity. This condition is related to Nielsen cores ofFuchsian groups. We use this to define the Fenchel-Nielsen Teichm\"uller spaceassociated to a geometric pair of pants decomposition. We study a metric onsuch a Teichm\"uller space, and we compare it to the quasiconformalTeichm\"uller space, equipped with the Teichm\"uller metric. We studyconditions under which there is an equality between these Teichm\"uller spacesand we study topological and metric properties of the identity map when thismap exists.

On Fenchel-Nielsen coordinates on Teichm\"uller spaces of surfaces of infinite type