Homology, Homotopy and Applications

Volume 24 (2022)

Number 1

Stability of Loday constructions

Pages: 245 – 269

DOI: https://dx.doi.org/10.4310/HHA.2022.v24.n1.a13


Ayelet Lindenstrauss (Department of Mathematics, Indiana University, Bloomington, In., U.S.A.)

Birgit Richter (Fachbereich Mathematik der Universität Hamburg, Germany)


We study the question for which commutative ring spectra $A$ the tensor of a simplicial set $X$ with $A, X \otimes A$, is a stable invariant in the sense that it depends only on the homotopy type of $\Sigma X$. We prove several structural properties about different notions of stability, corresponding to different levels of invariance required of $X \otimes A$.We establish stability in important cases, such as complex and real periodic topological K‑theory, $KU$ and $KO$.


Loday construction, stability, topological Hochschild homology, commutative ring spectrum

2010 Mathematics Subject Classification

18G60, 55P43

Received 28 April 2020

Received revised 6 May 2021

Accepted 8 May 2021

Published 13 April 2022