In a city where racial divisions are an open sore as raw as anywhere in the country, New York's mayors are doomed to be defined by racial strife.

Howard Beach summed up the years of coded insults directed at the city's black and Latino residents during the Koch years. Crown Heights fixed an image of David Dinkins as a remote and ineffectual leader who was slow to crack down on black criminals.

Now, as we enter the last months of Rudolph Giuliani's first term, comes the torture of a Haitian immigrant at the hands of white police officers in Brooklyn.

Anyone who has been in a precinct house knows that what happened to Abner Louima can not be explained as the isolated action of a couple of officers run amuck. The idea that a man can have a wooden rod rammed up his rectum and then have his teeth knocked out with the bloody, excrement-covered club without the other officers on duty knowing it is absurd. The cover-up that followed can only be explained as a precinct-wide conspiracy.

No one can doubt the genuine horror and revulsion Mayor Giuliani feels at the disgusting brutalization of Abner Louima. But this horrible incident is the culmination of years of giving police officers accused of brutality and racism the benefit of the doubt. It is consistent with the Mayor's macho public persona and with his Police Department's policy of rewarding officers who project an unyielding, no-nonsense image that mirrors the Mayor's own.

Police officers know what all New Yorkers know: that Giuliani's New York is a better place for white people than for black people. They know that for four years Mr. Giuliani has rejected efforts to create an independent investigative agency to respond to accusations of police misconduct. They know that he admires toughness and swagger.

In subtle and not-so-subtle fashions, mayors set the tone for the city's police force. If Crown Heights was the culmination of David Dinkins' tread-softly policy, Brooklyn's 70th Precinct is where Rudolph Giuliani's chickens have come home to roost.

Brutalizing a prisoner with a washroom plunger may be beyond the pale, but a Mayor who himself bristles and attacks at any suggestion of criticism ought not to be too surprised when a young man in a blue uniform figures his fists or his night stick are an appropriate response to a show of disrespect.

A man who delivered a profane address to a rally of off-duty police officers, as Mr. Giuliani did at the start of the 1992 campaign--a rally where unruly officers referred to Mayor Dinkins as "that washroom attendant"--ought not to be shocked when officers hurl racial slurs at people they consider criminals or low-lifes.

According to Mr. Louima, one of his assailants summed up the police culture succinctly. As he shoved the plunger into Mr. Louima's rectum, he told him, "This is Giuliani time, not Dinkins time."

Our city needs a mayor--either this one or another one--able to admit that black and Latino New Yorkers are as likely to fear the police as to welcome them. It needs a mayor who wants to change that. It needs a mayor who wants his or her time to be a time of healing, not a time of fear.