Formality of the Little N-Disks Operad

Released on by Pascal Lambrechts
preview-18

  • Formality of the Little N-Disks Operad Book Detail

  • Author : Pascal Lambrechts
  • Release Date : 2014-09-11
  • Publisher :
  • Genre : MATHEMATICS
  • Pages : 130
  • ISBN 13 : 9781470416690
  • File Size : 58,58 MB
DOWNLOAD BOOK

Formality of the Little N-Disks Operad by Pascal Lambrechts PDF Summary

Book Description: The little $N$-disks operad $\mathcal B$ along with its variants is an important tool in homotopy theory. It is defined in terms of configurations of disjoint $N$-dimensional disks inside the standard unit disk in $\mathbb{R} DEGREESN$ and it was initially conceived for detecting and understanding $N$-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 $N$-disks operad over the field of real numbers. More precisely one can consider the singular chains $\operatorname{C}_*(\mathcal B; \mathbb{R})$ on $\mathcal B$ as well as the singular homology $\operatorname{H}_*(\mathcal B; \mathbb{R})$ of $\mathcal B$. 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 $m$-disks operad in the little $N$-disks operad when $N\ge

Disclaimer: www.yourbookbest.com does not own Formality of the Little N-Disks Operad books pdf, neither created or scanned. We just provide the link that is already available on the internet, public domain and in Google Drive. If any way it violates the law or has any issues, then kindly mail us via contact us page to request the removal of the link.