If he's the father he has a right to see his child (and the child has a right to a relationship with his father). You can deny his paternity and force him to go to court for a DNA test before giving him access to the baby,but it sounds as though he wouldn't bother.
Talk to a lawyer, or someone at a legal-aid clinic. Probably the laws are different in different places. I don't think it is up to you to stay in touch, it would be up to him to approach you and try to make that happen, if he wants parental rights.