NYPD detectives have arrested a 21-year-old man for randomly stabbing a young woman in the back inside a Chelsea subway station during a disturbing, unprovoked attack, police said Friday.

Carlos Rivera said nothing to his 25-year-old victim as he jammed a blade into her side as she descended a flight of stairs at the W. 23rd St. station during rush hour Tuesday, court documents show. Rivera was standing in the middle of the staircase and knifed her as she walked past. No one else was on the stairs at the time, cops said.

After the 6:30 p.m. stabbing, Rivera calmly put up his hood and exited the station, again saying nothing, prosecutors said Friday as they arraigned him on attempted murder and assault charges.

His victim didn’t realize she had been stabbed until she reached the bott

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