# 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} }

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…

## 3 Citations

### Twisted IBL-infinity-algebra and string topology: First look and examples

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We study the application of IBL-infinity-algebras to string topology and explicitly compute the case of spheres. This involves finding a Green kernel and computing integrals associated to trivalent…

### Cumulants, Koszul brackets and homological perturbation theory for commutative $BV_\infty$ and $IBL_\infty$ algebras

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We explore the relationship between the classical constructions of cumulants and Koszul brackets, showing that the former are an expontial version of the latter. Moreover, under some additional…

### A distributive law for compact symmetric multicategories

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Compact symmetric multicategories (CSMs) generalise a number of operad-like devices, such as wheeled properads and modular operads, that admit a contraction operation as well as an operadic…

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