Homology, Homotopy and Applications

Volume 23 (2021)

Number 1

Truncated derived functors and spectral sequences

Pages: 159 – 189

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n1.a10

Authors

Hans-Joachim Baues (Max-Planck-Institut für Mathematik, Bonn, Germany)

David Blanc (Department of Mathematics, University of Haifa, Israel)

Boris Chorny (Department of Mathematics, University of Haifa at Oranim, Tivon, Israel)

Abstract

The $E_2$-term of the Adams spectral sequence may be identified with certain derived functors, and this also holds for a number of other spectral sequences. Our goal is to show how the higher terms of such spectral sequences are determined by truncations of relative derived functors, defined in terms of certain simplicial functors called mapping algebras.

Keywords

spectral sequence, relative derived functor, truncation, differential, (co)simplicial resolution, mapping algebra

2010 Mathematics Subject Classification

Primary 55T99. Secondary 18C30, 18G50, 55U35.

Received 20 October 2019

Accepted 11 May 2020

Published 2 September 2020