Cylinders for non-symmetric DG-operads via homological perturbation theory

TL;DR

This paper develops a method to construct small cylinders for cellular non-symmetric DG-operads over any commutative ring using homological perturbation, enabling new insights into A-infinity operads and related structures.

Contribution

It introduces a novel construction of small cylinders for non-symmetric DG-operads via homological perturbation, applicable over arbitrary rings.

Findings

Constructed small cylinders for cellular non-symmetric DG-operads.

Applied the construction to the A-infinity operad to parametrize identity-linear maps.

Computed examples with non-trivial operations in low arities.

Abstract

We construct small cylinders for cellular non-symmetric DG-operads over an arbitrary commutative ring by using the basic perturbation lemma from homological algebra. We show that our construction, applied to the A-infinity operad, yields the operad parametrizing A-infinity maps whose linear part is the identity. We also compute some other examples with non-trivial operations in arities 1 and 0.