As you told, cervical cancer and related issues are caused by HPV infections. HPVs are of more than 70 types and are usually seen transmitted through sexual contact. But in contrary to the popular belief, it is spread through skin to skin contact with one having genital warts or particularly HPV infection. It happens when HPV virus from superficial cells of an infected person gets into a non-infected person. Usually, wart caused by infection is seen decanting by course of time. So, ultimately, sexual contact is not absolutely necessary for a spread. But it is yet to be discovered, how long the virus can live in non-living surfaces of skin and on other media. Treatments are available and you may consider getting some, if the warts are not disappearing even after a year. Take care.