Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Butterflies II: Torsors for 2-group stacks Ettore Aldrovandi
 

Summary: Butterflies II: Torsors for 2-group stacks
Ettore Aldrovandi
Department of Mathematics, Florida State University
1017 Academic Way, Tallahassee, FL 32306-4510, USA
aldrovandi@math.fsu.edu
Behrang Noohi
Department of Mathematics, King's College London
Strand, London WC2R 2LS, UK
behrang.noohi@kcl.ac.uk
Abstract
We study torsors over 2-groups and their morphisms. In particular, we
study the first non-abelian cohomology group with values in a 2-group.
Butterfly diagrams encode morphisms of 2-groups and we employ them to
examine the functorial behavior of non-abelian cohomology under change
of coefficients. We re-interpret the first non-abelian cohomology with
coefficients in a 2-group in terms of gerbes bound by a crossed module. Our
main result is to provide a geometric version of the change of coefficients
map by lifting a gerbe along the "fraction" (weak morphism) determined by
a butterfly. As a practical byproduct, we show how butterflies can be used
to obtain explicit maps at the cocycle level. In addition, we discuss various

  

Source: Aldrovandi, Ettore - Department of Mathematics, Florida State University

 

Collections: Mathematics