• Corpus ID: 119734545

Properads and Homotopy Algebras Related to Surfaces

@article{Doubek2017ProperadsAH,
  title={Properads and Homotopy Algebras Related to Surfaces},
  author={Martin Doubek and Branislav Jur{\vc}o and Lada Peksov{\'a}},
  journal={arXiv: Algebraic Topology},
  year={2017}
}

• M. Doubek, B. Jurčo, Lada Peksová
• Published 3 August 2017
• Mathematics
• arXiv: Algebraic Topology

Starting from a biased definition of a properad, we describe explicitly algebras over the cobar construction of a properad. Equivalent description in terms of solutions of generalized master equations, which can be interpreted as homological differential operators, are explained from the properadic point of view. This is parallel to the Barannikov's theory for modular operads. In addition to well known IBL-homotopy algebras, the examples include their associative analogues, which we call $IBA$-homotopy algebras, and a combination of the above two.