Is is legal to neuter a cat that doesn't belong to you?

I have lived in my apartment for about a year now and the cat situation is rampant, we knew this even when we moved in here. I never really had a problem with it until this last spring when all the kittens came out. It has gotten out of control and all the neighbors seem to do is feed them which is good but they never try to get them in and get them neutered at least. Recently one of the cats ran inside my house he was young and had a terrible mite infestation and his ears were draining puss so I took him to the vet and had him neutered and his ears cleaned out and gave him antibiotics for the infection. No one claimed him so I decided to keep him. Now there is a new cat hanging around my apartment and although I have seen this one before, he is much older possibly the little ones dad, I have never seen him belong to anybody, he always seemed very skittish and almost seemed feral like all the other cats. He has been following me around my apartment complex and sleeps outside my bedroom window. I noticed him and felt bad so I gave him a little food when he waited for me outside my door one day and I noticed he had a lot of mats so I cut them out because they were beyond brushing. He is not neutered and I know even if he is a stray he should be neutered but im worried if I do that and he does belong to somebody I could be in a lot of trouble. He is always outside and he always comes to me so I know I could get him to the vet without trapping him. If he is outside and with no collar can I neuter him without owner consent if he does belong to somebody? Thank you