| Title:
|
Properads and homological differential operators related to surfaces (English) |
| Author:
|
Peksová, Lada |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
54 |
| Issue:
|
5 |
| Year:
|
2018 |
| Pages:
|
299-312 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a biased definition of a properad and an explicit example of a closed Frobenius properad. We recall the construction of the cobar complex and algebra over it. We give an equivalent description of the algebra in terms of Barannikov’s theory which is parallel to Barannikov’s theory of modular operads. We show that the algebra structure can be encoded as homological differential operator. Example of open Frobenius properad is mentioned along its specific properties. (English) |
| Keyword:
|
properads |
| Keyword:
|
Frobenius properad |
| Keyword:
|
cobar complex |
| Keyword:
|
Barannikov’s type theory |
| Keyword:
|
homological differential operators |
| MSC:
|
18D50 |
| idZBL:
|
Zbl 06997357 |
| idMR:
|
MR3887356 |
| DOI:
|
10.5817/AM2018-5-299 |
| . |
| Date available:
|
2018-12-06T16:17:11Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147506 |
| . |
| Reference:
|
[1] Barannikov, S.: Modular operads and Batalin-Vilkovisky geometry.Internat. Math. Res. Notices (2007), Article ID rnm075, 31 pages. MR 2359547 |
| Reference:
|
[2] Doubek, M., Jurčo, B., Münster, K.: Modular operads and the quantum open-closed homotopy algebra.J. High Energy Phys. (2015), Article ID 158 (2015), arXiv:1308.3223 [math.AT]. MR 3464644 |
| Reference:
|
[3] Drummond-Cole, G.C., Terilla, J., Tradler, T.: Algebras over Cobar(coFrob).J. Homotopy Relat. Struct. 5 (1) (2010), 15–36, arXiv:0807.1241 [math.QA]. MR 2591885 |
| Reference:
|
[4] Getzler, E., Kapranov, M.M.: Modular operads.Compositio Math. 110 (1) (1998), 65–126, arXiv:dg-ga/9408003. MR 1601666, 10.1023/A:1000245600345 |
| Reference:
|
[5] Hackney, P., Robertson, M., Yau, D.: Infinity Properads and Infinity Wheeled Properads.Lecture Notes in Math., Springer International Publishing, 2015. MR 3408444 |
| Reference:
|
[6] Markl, M., Shnider, S., Stasheff, J.: Operads in algebra, topology and physics.Math. Surveys Monogr., vol. 96, Amer. Math. Soc., Providence, RI, 2002. Zbl 1017.18001, MR 1898414 |
| Reference:
|
[7] Merkulov, S., Vallette, B.: Deformation theory of representations of prop(erad)s I.J. Reine Angew. Math. 634 (2009), 51–106. MR 2560406 |
| Reference:
|
[8] Münster, K., Sachs, I.: Quantum open-closed homotopy algebra and string field theory.Comm. Math. Phys. 321 (3) (2013), 769–801, arXiv:1109.4101 [hep-th]. MR 3070036, 10.1007/s00220-012-1654-1 |
| Reference:
|
[9] Peksová, L.: Algebras over operads and properads.Master's thesis, Charles Univ. Prague, 2016, https://is.cuni.cz/studium/dipl_uc/index.php?id=40d829716c2891d12550d202e189ef4e&tid=1&do=xdownload&fid=120229648&did=148219&vdetailu=1. |
| Reference:
|
[10] Vallette, B.: A Koszul duality for props.Trans. Amer. Math. Soc. 359 (10) (2007), 4865–4943, arXiv:math/0411542. MR 2320654, 10.1090/S0002-9947-07-04182-7 |
| . |
