Class Notes Math 654 (fall 2015)


The first algebraic tool that you learned about for distinguishing spaces is the fundamental group π 1 (X). As you saw, this is already sufficient for distinguishing surfaces. But this tool has several drawbacks: (1) It fails to distinguish many spaces. For example, S 2 and S 3 are both simply-connected but are not homotopy equivalent. (2) It is in practice… (More)


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