| Title:
|
How to discretize the differential forms on the interval (English) |
| Author:
|
Bandiera, Ruggero |
| Author:
|
Schätz, Florian |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
1 |
| Issue:
|
1 |
| Year:
|
2017 |
| Pages:
|
56-86 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We provide explicit quasi-isomorphisms between the following three algebraic structures associated to the unit interval: i) the commutative dg algebra of differential forms, ii) the non-commutative dg algebra of simplicial cochains and iii) the Whitney forms, equipped with a homotopy commutative and homotopy associative, i.e. $C_\infty$, algebra structure. Our main interest lies in a natural ‘discretization’ $C_\infty$ quasi-isomorphism $\phi$ from differential forms to Whitney forms. We establish a uniqueness result that implies that $\phi$ coincides with the morphism from homotopy transfer, and obtain several explicit formulas for $\phi$, all of which are related to the Magnus expansion. In particular, we recover combinatorial formulas for the Magnus expansion due to Mielnik and Pleba\'nski. (English) |
| Keyword:
|
Homotopical algebra |
| Keyword:
|
rational homotopy theory |
| Keyword:
|
Eulerian idempotent |
| Keyword:
|
Magnus expansion |
| Keyword:
|
iterated integrals |
| MSC:
|
18G55 |
| MSC:
|
55P62 |
| idZBL:
|
Zbl 1410.18018 |
| idMR:
|
MR3912051 |
| DOI:
|
10.21136/HS.2017.03 |
| . |
| Date available:
|
2026-03-10T10:33:49Z |
| Last updated:
|
2026-03-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153394 |
| . |
| Reference:
|
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| . |
