Authorities say the suspect, also 62, stabbed the woman inside the lobby of Jerome L. Greene Hall, a law school building on West 116th Street just before 4 p.m. Thursday.
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The victim was stabbed multiple times, including in the right breast, right thigh, right shoulder, across her neck and in her right hand.
She was taken to Mount Sinai Morningside Hospital in stable condition.
The suspect is in custody with charges pending.
A kitchen knife was recovered.
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The two women know each other and neither are affiliated with Columbia University, although the suspect's daughter is a student.
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