Mahanta, Kuwari2024-02-052024-02-052024ROLL No.176123007https://gyan.iitg.ac.in/handle/123456789/2544Supervisor: Palaparthi, SreekrishnaLet Sg denote a closed, orientable surface of genus g 2. Let C(Sg) be the associated curve graph and d be the associated path metric. Let and be curves on Sg and T ( ) be the Dehn twist of about .enThesis