| Title:
|
An A_$\infty$-version of the Eilenberg-Moore theorem (English) |
| Author:
|
Franz, Matthias |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
9 |
| Issue:
|
2 |
| Year:
|
2025 |
| Pages:
|
136-167 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct an A_$\infty$-structure on the two-sided bar construction involving homotopy Gerstenhaber algebras (hgas). It extends the non-associative product defined by Carlson and the author and generalizes the dga structure on the one-sided bar construction due to Kadeishvili-Saneblidze. As a consequence, the multiplicative cohomology isomorphism from the Eilenberg-Moore theorem is promoted to a quasi-isomorphism of A_$\infty$-algebras. We also show that the resulting product on the differential torsion product involving cochain algebras agrees with the one defined by Eilenberg-Moore and Smith, for all triples of spaces. This is a consequence of the following result, which is of independent interest: The strongly homotopy commutative (shc) structure on cochains inductively constructed by Gugenheim-Munkholm agrees with the one previously defined by the author for all hgas. (English) |
| Keyword:
|
Eilenberg–Moore theorem |
| Keyword:
|
bar construction |
| Keyword:
|
A_$\infty$-algebra |
| Keyword:
|
homotopy Gerstenhaber algebra |
| Keyword:
|
shc algebra |
| MSC:
|
16E45 |
| MSC:
|
55R20 |
| MSC:
|
55T20 |
| idMR:
|
MR4994253 |
| DOI:
|
10.21136/HS.2025.13 |
| . |
| Date available:
|
2026-03-13T14:52:06Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153495 |
| . |
| Reference:
|
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