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nijenhuis infinity and contractible differential graded manifolds

  • s. a. merkulov (a1)
Abstract

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.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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