| Title:
|
Non-formality of $S^2$ via the free loop space (English) |
| Author:
|
McGowan, Ryan |
| Author:
|
Naef, Florian |
| Author:
|
O'Callaghan, Brian |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
9 |
| Issue:
|
2 |
| Year:
|
2025 |
| Pages:
|
198-210 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that the $E_1$-equivalence $C^{\bullet}(S^{2}) \simeq H^{\bullet}(S^{2})$ does not intertwine the inclusion of constant loops into the free loop space $S^2 \rightarrow LS^2$. That is, the isomorphism $HH_{\bullet}(H^{\bullet}(S^2)) \simeq H^{\bullet}(LS^2)$ does not preserve the obvious maps to $H^{\bullet}(S^{2})$ that exist on both sides. We give an explicit computation of the defect in terms of the $E_{\infty}$-structure on $C^{\bullet}(S^{2})$. Finally, we relate our calculation to recent work of Poirier-Tradler on the string topology of $S^2$. (English) |
| Keyword:
|
string topology |
| Keyword:
|
algebraic topology |
| Keyword:
|
operads |
| Keyword:
|
free loop space |
| MSC:
|
16E40 |
| MSC:
|
18M80 |
| MSC:
|
55P35 |
| MSC:
|
55P50 |
| idMR:
|
MR4994255 |
| DOI:
|
10.21136/HS.2025.15 |
| . |
| Date available:
|
2026-03-13T14:53:50Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153497 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| . |
