Truncated Derived Functors and Spectral Sequences

HANS JOACHIM BAUES; DAVID BLANC; BORIS CHORNY

doi:https://doi.org/10.4310/HHA.2021.V23.N1.A10

Truncated Derived Functors and Spectral Sequences

HANS JOACHIM BAUES, DAVID BLANC, BORIS CHORNY

Department of Mathematics

University of Haifa

Research output: Contribution to journal › Article › peer-review

Abstract

The E₂-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.

Original language	American English
Pages (from-to)	159-189
Number of pages	31
Journal	Homology, Homotopy and Applications
Volume	23
Issue number	1
DOIs	https://doi.org/10.4310/HHA.2021.V23.N1.A10
State	Published - 2021

Keywords

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

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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https://doi.org/10.4310/HHA.2021.V23.N1.A10

Cite this

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title = "Truncated Derived Functors and Spectral Sequences",

abstract = "The E2-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 = "(co)simplicial resolution, differential, mapping algebra., relative derived functor, spectral sequence, truncation",

author = "BAUES, {HANS JOACHIM} and DAVID BLANC and BORIS CHORNY",

note = "Funding Information: The research of the second and third authors was partially supported by Israel Science Foundation grants 770/16 and 1138/16, respectively. They regret that Hans Baues, a longtime friend and collaborator, passed away shortly after the final version of this paper was completed. Publisher Copyright: {\textcopyright} 2020. 2020, International Press. Permission to copy for private use granted. All Rights Reserved.",

year = "2021",

doi = "https://doi.org/10.4310/HHA.2021.V23.N1.A10",

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AU - BAUES, HANS JOACHIM

AU - BLANC, DAVID

AU - CHORNY, BORIS

N1 - Funding Information: The research of the second and third authors was partially supported by Israel Science Foundation grants 770/16 and 1138/16, respectively. They regret that Hans Baues, a longtime friend and collaborator, passed away shortly after the final version of this paper was completed. Publisher Copyright: © 2020. 2020, International Press. Permission to copy for private use granted. All Rights Reserved.

PY - 2021

Y1 - 2021

N2 - The E2-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.

AB - The E2-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.

KW - (co)simplicial resolution

KW - differential

KW - mapping algebra.

KW - relative derived functor

KW - spectral sequence

KW - truncation

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U2 - https://doi.org/10.4310/HHA.2021.V23.N1.A10

DO - https://doi.org/10.4310/HHA.2021.V23.N1.A10

M3 - Article

SN - 1532-0073

VL - 23

SP - 159

EP - 189

JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

IS - 1

ER -

Truncated Derived Functors and Spectral Sequences

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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