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Feb 16, 2017 at 18:14 comment added Sebastian Goette Indeed, I found the example by looking at the corresponding part of the homology exact sequence. But then dimension 2 was sufficient to realise it, so I had to discuss the fundamental group, too. But I am confused about the the last statement: in order to loose connectivity, we need the map to be not surjective on homology. Is that what you meant? In the example above, the map induces multiplication by 2 or 3 in $\mathbb Z$.
Feb 16, 2017 at 14:28 history answered Jeff Strom CC BY-SA 3.0