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For questions requesting examples of a certain structure or phenomenon

15 votes

Satellite knot example

Examples for this are easy to find, such as the Whitehead double of the figure eight knot. …
Allen Hatcher's user avatar
34 votes
Accepted

Are there pairs of highly connected finite CW-complexes with the same homotopy groups?

Here is a method for constructing examples. … Perhaps there are simpler examples. It might be interesting to find examples where just homology suffices to distinguish the two spaces. …
Allen Hatcher's user avatar
31 votes
Accepted

Fundamental group of the line with the double origin.

The earlier answers showing that the fundamental group of this space is infinite cyclic by determining its universal cover or by constructing a fiber bundle over it with contractible fibers are very n …
Allen Hatcher's user avatar