| Title:
|
Modular operads with connected sum and Barannikov’s theory (English) |
| Author:
|
Peksová, Lada |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
56 |
| Issue:
|
5 |
| Year:
|
2020 |
| Pages:
|
287-300 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the connected sum for modular operads. This gives us a graded commutative associative product, and together with the BV bracket and the BV Laplacian obtained from the operadic composition and self-composition, we construct the full Batalin-Vilkovisky algebra. The BV Laplacian is then used as a perturbation of the special deformation retract of formal functions to construct a minimal model and compute an effective action. (English) |
| Keyword:
|
modular operads |
| Keyword:
|
connected sum |
| Keyword:
|
Batalin-Vilkovisky algebra |
| Keyword:
|
homological perturbation lemma |
| MSC:
|
18D50 |
| MSC:
|
81T99 |
| idZBL:
|
Zbl 07285966 |
| idMR:
|
MR4188743 |
| DOI:
|
10.5817/AM2020-5-287 |
| . |
| Date available:
|
2020-11-20T13:57:47Z |
| Last updated:
|
2021-02-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148439 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Doubek, M., Jurčo, B., Peksová, L., Pulmann, J.: Quantum homotopy algebras.in preparation. |
| Reference:
|
[5] Doubek, M., Jurčo, B., Pulmann, J.: Quantum $L_\infty $ algebras and the homological perturbation lemma.Comm. Math. Phys. 367 (1) (2019), 215–240. MR 3933409, 10.1007/s00220-019-03375-x |
| Reference:
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| Reference:
|
[7] Markl, M.: Loop homotopy algebras in closed string field theory.Comm. Math. Phys. 221 (2) (2001), 367–384. MR 1845329, 10.1007/PL00005575 |
| Reference:
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[8] Schwarz, A.: Geometry of Batalin-Vilkovisky quantization.Comm. Math. Phys. 155 (2) (1993), 249–260. Zbl 0786.58017, MR 1230027, 10.1007/BF02097392 |
| Reference:
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| . |
