Your question leaves out some details that would make the answer a bit more complete. If you left New York to come here, and he remained, then New York would maintain jurisdiction over all issues -- including alimony -- as the State of last matrimonial domicile. If that seems confusing, see the explanation detailed in the article titled "The Basics of Family Law Jurisdiction," on the Published Works page of our firm web site, at http://www.willicklawgroup.com/published_works.
If you do not want the orders requested in the Complaint to be entered, then you will have to oppose the Complaint in New York.
If you did NOT leave New York to come here, then the New York courts would have authority to dissolve the marriage, but not much else (essentially, over property in the jurisdiction, but for details, speak with a New York lawyer.
I realize that you don't have a job, but I think it very important that you find someone in New York to advise you -- they probably have some version of a pro bono project to reduced fee panel there, as we do here. You should probably seek consultation with an appropriate family law specialist. I would suggest starting your search with the American Academy of Matrimonial Lawyers, which can be viewed at http://www.aaml.org. Good luck.
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