Contents Online

# Homology, Homotopy and Applications

## Volume 4 (2002)

### Number 1

### The Taylor towers for rational algebraic $K$-theory and Hochschild homology

Pages: 191 – 212

DOI: http://dx.doi.org/10.4310/HHA.2002.v4.n1.a11

#### Authors

#### Abstract

We compute the Taylor tower for Hochschild homology as a functor from augmented commutative simplicial $\mathbb{Q}$-algebras, to chain complexes over $\mathbb{Q}$. We use this computation to obtain the layers for the Taylor tower of rational algebraic $K$-theory. We also show that the Hodge decomposition for rational Hochschild homology is the decomposition of the Taylor tower of the augmentation ideal functor into its homogeneous layers when evaluated at a suspension.

#### Keywords

Goodwillie calculus, Rational algebraic $K$-theory, Hochschild homology, Hodge decomposition

#### 2010 Mathematics Subject Classification

13D03, 19D55, 55Uxx