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nijenhuis infinity and contractible differential graded manifolds

Published online by Cambridge University Press:  01 September 2005

s. a. merkulov
Affiliation:
matematiska institutionen, stockholm universitet, 10691 stockholm, swedensm@math.su.se
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Abstract

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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.

Type
Research Article
Copyright
foundation compositio mathematica 2005