There exist several cobordisms, and the one I am interested in is oriented cobordism. This is because fixing an orientation is necessary to define a degree. Maybe this question can help to understand why this is a good definition.

]]>Thanks for your time to answer. See, I’m having trouble understanding why is that is your definition. Milnor just says the boundary is the union of the two manifolds product and , without any regards to opposite orientation. Could you, please, explain where doe the minus sign come from?

]]>This follows from the definition of a cobordism: is a copy of and a copy of , ie., the orientation of is reversed.

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