Geodesic
Modular operads with connected sum and Barannikov’s theory
Archivum mathematicum, Tome 56 (2020) no. 5, pp. 287-300

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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.
DOI : 10.5817/AM2020-5-287
Classification : 18D50, 81T99
Keywords: modular operads; connected sum; Batalin-Vilkovisky algebra; homological perturbation lemma 
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Peksová, Lada. Modular operads with connected sum and Barannikov’s theory. Archivum mathematicum, Tome 56 (2020) no. 5, pp. 287-300. doi: 10.5817/AM2020-5-287

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