Michael Polding, 63, was found dead in his flat on 16 July by officers who went there because no-one had seen him, Sussex Police said.
Mr Polding, who was openly gay, had only moved to the Kemp Town area of Brighton from London, nine months previously, and detectives have said they were trying to build a picture of his lifestyle.
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Hide AdA post-mortem examination confirmed the dead man had suffered injuries and, although he has not been formally identified, police believe the body to be that of Mr Polding.
A 28-year-old man from London was arrested on suspicion of murder and has been brought to Sussex for questioning.
Detective Chief Inspector Nick May, who is leading the inquiry, said: “We are continuing to put together a picture of the circumstances surrounding Mr Polding’s death and how he sustained his injuries.”