The incident happened over the weekend.
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Police said a man took a pair of sunglasses from a display in Times Square without paying.
Then the man allegedly swung a piece of broken glass at the vendor before taking off.
Footage from the officer's body camera shows him chasing the suspect down a street, staying hot on his trail. At one point, the officer and his horse weaved in and out of traffic along the street.
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The suspect was ultimately arrested.
He's being charged with robbery, menacing, and criminal possession of a weapon.