Timeline for Torsion in homology or fundamental group of subsets of Euclidean 3-space
Current License: CC BY-SA 4.0
21 events
| when toggle format | what | by | license | comment | |
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| S Sep 16 at 1:03 | history | bounty ended | CommunityBot | ||
| S Sep 16 at 1:03 | history | notice removed | CommunityBot | ||
| S Sep 7 at 23:58 | history | bounty started | Ali Taghavi | ||
| S Sep 7 at 23:58 | history | notice added | Ali Taghavi | Draw attention | |
| Sep 1 at 23:00 | comment | added | Ali Taghavi | In fact I meant the closure of unbounded open contractible sets, sorry I forget the "contractible" in previous comment" | |
| Sep 1 at 10:11 | comment | added | Ali Taghavi | Is the problem obvious for the closure of open unbounded subsets of $\mathbb{R}^3$? | |
| Jan 21, 2022 at 1:08 | history | edited | YCor | CC BY-SA 4.0 |
fixed assumption (1 has finite order, and "torsion-free" is a standard terminology)
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| Feb 22, 2021 at 22:27 | comment | added | John Samples | Yup, that's the one! It's a great paper; maybe not the biggest result in the world, but it's just such a pleasure. | |
| Feb 22, 2021 at 21:42 | comment | added | Jeremy Brazas | @JohnSamples I bet you're thinking of Ziga Virk's paper for countable groups $G$. This is a nice result but unfortunately it doesn't doesn't provide much for the $\mathbb{R}^3$ situation. I'll go ahead and add here that shape/Cech invariants will also be pretty unhelpful to this problem since there many subsets with trivial shape and uncountable first singular homology. | |
| Feb 22, 2021 at 20:07 | answer | added | Moishe Kohan | timeline score: 2 | |
| Feb 9, 2021 at 19:38 | comment | added | John Samples | There's a continuum in $\mathbb{R}^4$ such that for an arbitrary group $G$, it has a subspace with fundamental group $G$. I had trouble finding the paper (it's pretty recent, maybe 5ish years old?), but my idea would be to read that paper and see if anything they did happens to live in $\mathbb{R}^3$, perhaps after a well-chosen quotient. It'd surprise me if you could get ANYTHING in dimension $4$, but NOTHING in dimension $3$. Maybe someone with better Googling skills can link the paper, at least. | |
| Jun 18, 2019 at 18:36 | history | edited | Ian Agol | CC BY-SA 4.0 |
deleted 1 character in body
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| Jun 18, 2019 at 14:46 | answer | added | Jeffrey Rolland | timeline score: 0 | |
| Nov 19, 2010 at 19:45 | history | edited | Ryan Budney | CC BY-SA 2.5 |
corrected previous oversight
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| Nov 13, 2010 at 23:43 | answer | added | Sergey Melikhov | timeline score: 19 | |
| Jul 13, 2010 at 18:04 | answer | added | BS. | timeline score: 9 | |
| Nov 7, 2009 at 2:17 | history | edited | Ryan Budney | CC BY-SA 2.5 |
update description because of observations in latter discussion
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| Nov 7, 2009 at 2:01 | answer | added | Igor Belegradek | timeline score: 7 | |
| Nov 7, 2009 at 1:51 | answer | added | Autumn Kent | timeline score: 14 | |
| Nov 7, 2009 at 1:40 | history | edited | Ryan Budney |
more tags
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| Nov 7, 2009 at 1:14 | history | asked | Ryan Budney | CC BY-SA 2.5 |