We give a cohomological criterion for the existence and uniqueness of solutions of the $2$-cocycle gluing problem
in block theory. The existence of a solution for the $2$-cocycle gluing problem is further reduced to a property
of fusion systems of certain finite groups associated with the fusion system of a block.
@article{1251832566,
author = {Linckelmann, Markus},
title = {On $H*(C; k$\times$)$ for fusion systems},
journal = {Homology Homotopy Appl.},
volume = {11},
number = {1},
year = {2009},
pages = { 203-218},
language = {en},
url = {http://dml.mathdoc.fr/item/1251832566}
}
Linckelmann, Markus. On $H*(C; k×)$ for fusion systems. Homology Homotopy Appl., Tome 11 (2009) no. 1, pp. 203-218. http://gdmltest.u-ga.fr/item/1251832566/