Formality of the Little $N$-disks Operad

Released on by Pascal Lambrechts
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  • Formality of the Little $N$-disks Operad Book Detail

  • Author : Pascal Lambrechts
  • Release Date : 2014-06-05
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 130
  • ISBN 13 : 0821892126
  • File Size : 37,37 MB
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Formality of the Little $N$-disks Operad by Pascal Lambrechts PDF Summary

Book Description: The little -disks operad, , along with its variants, is an important tool in homotopy theory. It is defined in terms of configurations of disjoint -dimensional disks inside the standard unit disk in and it was initially conceived for detecting and understanding -fold loop spaces. Its many uses now stretch across a variety of disciplines including topology, algebra, and mathematical physics. In this paper, the authors develop the details of Kontsevich's proof of the formality of little -disks operad over the field of real numbers. More precisely, one can consider the singular chains on as well as the singular homology of . These two objects are operads in the category of chain complexes. The formality then states that there is a zig-zag of quasi-isomorphisms connecting these two operads. The formality also in some sense holds in the category of commutative differential graded algebras. The authors additionally prove a relative version of the formality for the inclusion of the little -disks operad in the little -disks operad when .

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