Local-to-global spectral sequences for the cohomology of diagrams

David Blanc; Mark W. Johnson; James M. Turner

doi:10.1016/j.jpaa.2008.05.011

Local-to-global spectral sequences for the cohomology of diagrams

David Blanc
, Mark W. Johnson
, James M. Turner

Department of Mathematics

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

Abstract

We construct local-to-global spectral sequences for the cohomology of a diagram, which compute the cohomology of the full diagram in terms of smaller pieces. These are motivated by the obstruction theory of D. Blanc et al. [D. Blanc, M.W. Johnson, J.M. Turner, On realizing diagrams of Π-algebras, Algebraic Geom. Topol. 6 (2006) 763-807] for realizing a diagram of Π-algebras, but are valid in quite general algebraic settings.

Original language	English
Pages (from-to)	34-53
Number of pages	20
Journal	Journal of Pure and Applied Algebra
Volume	213
Issue number	1
DOIs	https://doi.org/10.1016/j.jpaa.2008.05.011
State	Published - Jan 2009

Bibliographical note

Funding Information:
We would like to thank the referee for his or her comments. This research was supported by BSF grant 2006039; the third author was also supported by NSF grant DMS-0206647 and a Calvin Research Fellowship (SDG).

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jpaa.2008.05.011

Cite this

@article{1f0dba37a68046ae82e4a7259aa69c20,

title = "Local-to-global spectral sequences for the cohomology of diagrams",

abstract = "We construct local-to-global spectral sequences for the cohomology of a diagram, which compute the cohomology of the full diagram in terms of smaller pieces. These are motivated by the obstruction theory of D. Blanc et al. [D. Blanc, M.W. Johnson, J.M. Turner, On realizing diagrams of Π-algebras, Algebraic Geom. Topol. 6 (2006) 763-807] for realizing a diagram of Π-algebras, but are valid in quite general algebraic settings.",

author = "David Blanc and Johnson, \{Mark W.\} and Turner, \{James M.\}",

note = "Funding Information: We would like to thank the referee for his or her comments. This research was supported by BSF grant 2006039; the third author was also supported by NSF grant DMS-0206647 and a Calvin Research Fellowship (SDG). ",

year = "2009",

month = jan,

doi = "10.1016/j.jpaa.2008.05.011",

language = "English",

volume = "213",

pages = "34--53",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier",

number = "1",

}

TY - JOUR

T1 - Local-to-global spectral sequences for the cohomology of diagrams

AU - Blanc, David

AU - Johnson, Mark W.

AU - Turner, James M.

N1 - Funding Information: We would like to thank the referee for his or her comments. This research was supported by BSF grant 2006039; the third author was also supported by NSF grant DMS-0206647 and a Calvin Research Fellowship (SDG).

PY - 2009/1

Y1 - 2009/1

N2 - We construct local-to-global spectral sequences for the cohomology of a diagram, which compute the cohomology of the full diagram in terms of smaller pieces. These are motivated by the obstruction theory of D. Blanc et al. [D. Blanc, M.W. Johnson, J.M. Turner, On realizing diagrams of Π-algebras, Algebraic Geom. Topol. 6 (2006) 763-807] for realizing a diagram of Π-algebras, but are valid in quite general algebraic settings.

AB - We construct local-to-global spectral sequences for the cohomology of a diagram, which compute the cohomology of the full diagram in terms of smaller pieces. These are motivated by the obstruction theory of D. Blanc et al. [D. Blanc, M.W. Johnson, J.M. Turner, On realizing diagrams of Π-algebras, Algebraic Geom. Topol. 6 (2006) 763-807] for realizing a diagram of Π-algebras, but are valid in quite general algebraic settings.

UR - https://www.scopus.com/pages/publications/53549116734

U2 - 10.1016/j.jpaa.2008.05.011

DO - 10.1016/j.jpaa.2008.05.011

M3 - Article

AN - SCOPUS:53549116734

SN - 0022-4049

VL - 213

SP - 34

EP - 53

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 1

ER -

Local-to-global spectral sequences for the cohomology of diagrams

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this