2Gerbes bound by complexes of grstacks, and cohomology Ettore Aldrovandi Summary: 2­Gerbes bound by complexes of gr­stacks, and cohomology Ettore Aldrovandi Department of Mathematics, Florida State University Tallahassee, FL 32306­4510, USA aldrovandi@math.fsu.edu December 18, 2005 Abstract We define 2­gerbes bound by complexes of braided group­like stacks. We prove a classifica­ tion result in terms of hypercohomology groups with values in abelian crossed squares and cones of morphisms of complexes of length 3. We give an application to the geometric construction of certain elements in Hermitian Deligne cohomology groups. Contents Introduction 2 1 Background notions 7 1.1 Assumptions and notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Various Deligne complexes and cohomologies . . . . . . . . . . . . . . . . . . . . . 8 2 Gerbes with abelian band 10 2.1 Gerbes bound by a complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Further examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Collections: Mathematics