First of all, I apologize for the crudeness of my question. Consider the construction of the homotopy groups. We mod out the space of "loops" at point by the equivalence relation generated by homotopy equivalence then give the new space a group structure were the operation is "concatenation" of loops. My question: Could we, instead, mod out the space of "loops" (without reference to a specific point) by the equivalence relation generated by isotopy equivalence then give this space a group structure using some kind of "surgery" on the equivalence classes?
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