# nLab framed little n-disk operad

### Context

#### Higher algebra

higher algebra

universal algebra

# Contents

## Idea

The framed little $n$disk operad is an operad in chain complexes that whose $n$-ary operations come from embedding $n$-dimensional disks in a larger one and rotating them. It is joint generalization of the little k-cubes operad and the framed little 2-disk operad.

## Properties

###### Theorem

The shifted rational singular homology $H_{\bullet + d}(S X, \mathbb{Q})$ of the $n$-sphere space $S X = X^{S^n}$ of an oriented manifold $X$ of dimension $d$ naturally has the structure of a n-BV-algebra.

This appears as (CohenVoronov, theorem 5.3.3).

## References

Section 5.3 of

Created on November 26, 2010 16:47:52 by Urs Schreiber (131.211.36.78)