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Nov 5, 2022 at 0:25 comment added Ludwik Thanks for the info, I had read a comment of the connected sum of two immersions in C.T.C Wall's differential topology book, but I didn't find the definition of it. Fortunately, he does give a specific immersion of $S^n$ into $S^{2n}$ with a single self-intersection, and with that I have my problem solved.
Nov 5, 2022 at 0:20 vote accept Ludwik
Nov 4, 2022 at 21:09 history edited Roberto Ladu CC BY-SA 4.0
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Nov 4, 2022 at 18:18 history undeleted Roberto Ladu
Nov 4, 2022 at 18:17 history edited Roberto Ladu CC BY-SA 4.0
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Nov 4, 2022 at 17:32 history deleted Roberto Ladu via Vote
Nov 4, 2022 at 17:30 history answered Roberto Ladu CC BY-SA 4.0