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We prove, for any , that there is a closed connected orientable surface  so that the hyperbolic space  almost-isometrically embeds into the Teichmüller space of , with quasi-convex image lying in the thick part. As a consequence,  quasi-isometrically embeds in the curve complex of .
                    
                 
                
                    
                
            
        
        
        
            
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