nijenhuis infinity and contractible differential graded manifolds

[摘要] we find a minimal differential graded (dg) operad whose generic representations in ${mathbb r}^n$ are in one-to-one correspondence with formal germs of those endomorphisms of the tangent bundle to ${mathbb r}^n$ which satisfy the nijenhuis integrability condition. this operad is of a surprisingly simple origin: it is the cobar construction on the quadratic operad of homologically trivial dg lie algebras. as a by-product we obtain a strong-homotopy generalization of this geometric structure and show its homotopy equivalence to the structure of contractible dg manifolds.

[学科分类] 数学（综合）