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Feb 11, 2011 at 20:10 comment added Greg Kuperberg In the construction that I describe, you have to be careful to check that all cobordisms that you will need for the entire cobounding chain are available, and not just that your cycle is represented by a null-cobordant manifold.
Feb 11, 2011 at 19:29 comment added Ilya Grigoriev Thank you, your answer was very helpful. I'm especially hopeful because of your statement that cobordism is the only problem - I don't think it's a problem for me.
Feb 11, 2011 at 16:01 history answered Greg Kuperberg CC BY-SA 2.5