A Construction on Operads Applicable to Homology Operations and the Minimal Model

TL;DR

This paper introduces a novel operad construction that provides a new perspective on minimal models and reveals hidden algebraic structures in homology, enhancing understanding of homological operations.

Contribution

It presents a new operad construction that describes minimal models and uncovers nontrivial structures in homology of chain complexes.

Findings

New operad construction for minimal models

Algebraic structures on homology with trivial operad actions

Reveals hidden nontrivial structures in homology

Abstract

We define a construction on operads which yields a new description of the minimal model. The construction also allows us to define algebraic structures on the homology of chain complexes with homologously trivial operad algebra structures, thus exposing nontrivial structure where none is apparent.