Timeline for CW-complexes that cannot be homotopically compressed
Current License: CC BY-SA 4.0
13 events
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| Dec 1, 2021 at 12:25 | history | edited | Arshak Aivazian | CC BY-SA 4.0 |
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| Dec 1, 2021 at 11:24 | history | edited | Arshak Aivazian | CC BY-SA 4.0 |
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| Dec 1, 2021 at 11:08 | history | edited | Arshak Aivazian | CC BY-SA 4.0 |
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| Dec 1, 2021 at 10:58 | history | edited | Arshak Aivazian | CC BY-SA 4.0 |
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| Dec 1, 2021 at 10:46 | history | edited | Arshak Aivazian | CC BY-SA 4.0 |
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| Dec 1, 2021 at 10:14 | comment | added | Arshak Aivazian | I will add this type of contraction and edit the question accordingly - this seems to be a more natural formulation of the problem. | |
| Dec 1, 2021 at 10:04 | comment | added | Arshak Aivazian | Yes, my first statement is incorrect (when I wrote, I was thinking about contracting a spanning tree - factorization by contractible subspaces is also some special homotopy equivalence, but of a different kind) | |
| Dec 1, 2021 at 9:34 | comment | added | HJRW | I don't understand your claim 1. Consider, say, the theta graph or the barbell graph. (These are the two graphs of Euler characteristic -1 with every vertex of valence 3.) Neither contains the wedge of two circles as a subgraph (since neither contains a point of valence 4). Actually, my guess is that a graph is minimal in your sense if and only if it has no vertices of valence 1. | |
| Dec 1, 2021 at 9:23 | history | edited | Arshak Aivazian | CC BY-SA 4.0 |
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| Dec 1, 2021 at 9:17 | history | edited | Arshak Aivazian | CC BY-SA 4.0 |
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| Dec 1, 2021 at 9:14 | comment | added | Arshak Aivazian | @IJL Oh thanks, that was easy! Yes, I practically did not hope that CW-complexes are arranged so simply, but I did not think of how to refute it. | |
| Dec 1, 2021 at 9:11 | comment | added | IJL | Concerning the question at the end of your post: a wedge of $n$-manifolds will have top cohomology group a direct sum of $\mathbb{Z}$'s and $\mathbb{Z}/2$'s, so a mod-$p$ Moore space for $p$ an odd prime won't be of the form that you suggest. | |
| Dec 1, 2021 at 8:57 | history | asked | Arshak Aivazian | CC BY-SA 4.0 |