The short answer is yes, under certain circumstances, a website can render you subject to the jurisdiction of New York's courts. As noted in "How Websites Can Render a Manufacturer Subject to NY Jurisdiction," where a website targets New York consumers, and effectively transacts business there, the manufacturer may well be susceptible to being sued in New York if and when their product (allegedly) fails.

Jonathan Cooper
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Non-Compete, Trade Secret, Unfair Competition and School Negligence Lawyer