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.