Abstract
We introduce a Teichmuller space for a Riemann surface withn distinguished points. Ifn=0 this is the ordinary Teichmuller space. Forn=1, in special cases, it represents the Teichmuller curve and the universal covering space of the Teichmuller curve. The corresponding modular groups and Riemann spaces are investigated. Some purely topological applications on homotopy of self-maps of surfaces are obtained.
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