Modular operads with connected sum and Barannikov’s theory
Archivum Mathematicum (2020)
- Volume: 056, Issue: 5, page 287-300
- ISSN: 0044-8753
Access Full Article
top
Abstract
topHow to cite
topPeksová, Lada. "Modular operads with connected sum and Barannikov’s theory." Archivum Mathematicum 056.5 (2020): 287-300. <http://eudml.org/doc/297117>.
@article{Peksová2020,
abstract = {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.},
author = {Peksová, Lada},
journal = {Archivum Mathematicum},
keywords = {modular operads; connected sum; Batalin-Vilkovisky algebra; homological perturbation lemma},
language = {eng},
number = {5},
pages = {287-300},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Modular operads with connected sum and Barannikov’s theory},
url = {http://eudml.org/doc/297117},
volume = {056},
year = {2020},
}
TY - JOUR
AU - Peksová, Lada
TI - Modular operads with connected sum and Barannikov’s theory
JO - Archivum Mathematicum
PY - 2020
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 056
IS - 5
SP - 287
EP - 300
AB - 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.
LA - eng
KW - modular operads; connected sum; Batalin-Vilkovisky algebra; homological perturbation lemma
UR - http://eudml.org/doc/297117
ER -
References
top- Barannikov, S., Modular operads and Batalin-Vilkovisky geometry, Int. Math. Res. Not. IMRN 19 (2007), 31 pp., Art. ID rnm075. (2007) MR2359547
- Chuang, J., Lazarev, A., 10.1007/s11005-009-0314-7, Lett. Math. Phys. 89 (1) (2009), 33–49. (2009) MR2520178DOI10.1007/s11005-009-0314-7
- Doubek, M., Jurčo, B., Münster, K., Modular operads and the quantum open-closed homotopy algebra, J. High Energy Phys. 158 (12) (2015), 54 pp., Article ID 158. (2015) MR3464644
- Doubek, M., Jurčo, B., Peksová, L., Pulmann, J., Quantum homotopy algebras, in preparation.
- Doubek, M., Jurčo, B., Pulmann, J., 10.1007/s00220-019-03375-x, Comm. Math. Phys. 367 (1) (2019), 215–240. (2019) MR3933409DOI10.1007/s00220-019-03375-x
- Eilenberg, S., MacLane, S., On the groups . I, Ann. of Math. (2) 58 (1) (1953), 55–106. (1953) MR0056295
- Markl, M., 10.1007/PL00005575, Comm. Math. Phys. 221 (2) (2001), 367–384. (2001) MR1845329DOI10.1007/PL00005575
- Schwarz, A., 10.1007/BF02097392, Comm. Math. Phys. 155 (2) (1993), 249–260. (1993) Zbl0786.58017MR1230027DOI10.1007/BF02097392
- Zwiebach, B., 10.1006/aphy.1998.5803, Ann. Physics 267 (2) (1998), 193–248. (1998) MR1638333DOI10.1006/aphy.1998.5803
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.