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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
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Category: math
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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
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Date available: 2020-11-20T13:57:47Z
Last updated: 2021-02-23
Stable URL: http://hdl.handle.net/10338.dmlcz/148439
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Reference: [1] Barannikov, S.: Modular operads and Batalin-Vilkovisky geometry.Int. Math. Res. Not. IMRN 19 (2007), 31 pp., Art. ID rnm075. MR 2359547
Reference: [2] Chuang, J., Lazarev, A.: Abstract Hodge decomposition and minimal models for cyclic algebras.Lett. Math. Phys. 89 (1) (2009), 33–49. MR 2520178, 10.1007/s11005-009-0314-7
Reference: [3] 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. MR 3464644
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: [6] Eilenberg, S., MacLane, S.: On the groups $H(\Pi , n)$. I.Ann. of Math. (2) 58 (1) (1953), 55–106. MR 0056295
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: [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: [9] Zwiebach, B.: Oriented open-closed string theory revisited.Ann. Physics 267 (2) (1998), 193–248. MR 1638333, 10.1006/aphy.1998.5803
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