Modular operads with connected sum and Barannikov’s theory

Lada Peksová

Address: Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Prague, Czech Republic

E-mail: lada.peksova@gmail.com

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.

AMSclassification: primary 18D50; secondary 81T99.

Keywords: modular operads, connected sum, Batalin-Vilkovisky algebra, homological perturbation lemma.

DOI: 10.5817/AM2020-5-287