On Teichmuller spaces for surfaces of infinite type

Teichmuller spaces for surfaces of infinite type can be studied with geometric techniques, like the pair of pants decomposition and and Fenchel-Nielsen coordinates. In this case we have countably infinitely many pairs-of-pants and coordinates. With these techniques we can describe, under certain hypotheses, the topology given by the Teichmuller distance and the topology given by the "length spectrum" distance.