Title: Local-to-global spectral sequences for the cohomology of diagrams
Authors: David Blanc, Mark W. Johnson, and James M. Turner
E-mail: blanc@math.haifa.ac.il, mwj3@psu.edu, jturner@calvin.edu
Address: Department of Mathematics, University of Haifa, 31905 Haifa, Israel
Department of Mathematics, Penn State Altoona, Altoona, PA 16601, USA
Department of Mathematics, Calvin College, Grand Rapids, MI 49546, USA
arXiv:0802.4096
Abstract:
The cohomology of diagrams arises in various areas of mathematics, such
as deformation theory, classifying diagrams of groups, and in homotopy
theory, in the context of the rectification of homotopy-commutative
diagrams, and thus in the study of higher homotopy and cohomology operations.
For this purpose we construct ``local-to-global'' spectral sequences
for the cohomology of a diagram, which can be used to compute the
cohomology of the full diagram in terms of smaller pieces. We also
explain why such a local-to-global approach is relevant to higher
operations.