Fenchel-Nielsen coordinates on upper bounded pants decompositions

Let X-0 be an infinite-type hyperbolic surface (whose boundary components, if any, are closed geodesics) which has an upper bounded pants decomposition. The length spectrum Teichmuller space T-ls(X-0) consists of all surfaces X homeomorphic to X-0 such that the ratios of the corresponding simple closed geodesics are uniformly bounded from below and from above. Alessandrini, Liu, Papadopoulos and Su [1] described the Fenchel-Nielsen coordinates for T-ls(X-0) and using these coordinates they proved that T-ls(X-0) is path connected. We use the Fenchel-Nielsen coordinates for T-ls(X-0) to induce a locally bi-Lipschitz homeomorphism between l(infinity) and Tls(X-0) (which extends analogous results by Fletcher [9] and by Allessandrini, Liu, Papadopoulos, Su and Sun [2] for the unreduced and the reduced T-qc(X-0)). Consequently, T-ls(X-0) is contractible. We also characterize the closure in the length spectrum metric of the quasiconformal Teichmuller space T-qc(X-0) in T-ls(X-0).