Mathematics – Differential Geometry
Scientific paper
2010-07-21
Mathematics
Differential Geometry
34 pages
Scientific paper
A VB-groupoid is a vector-bundle object in the category of Lie groupoids. In this paper, we explain how VB-groupoids are the intrinsic geometric objects that correspond to 2-term representations up to homotopy of Lie groupoids. In particular, the tangent bundle of a Lie groupoid is a VB-groupoid that corresponds to the adjoint representations up to homotopy. The value of this point of view is that the tangent bundle is canonical, whereas the adjoint representations up to homotopy depend on a choice of connection. In the process of describing the correspondence between VB-groupoids and representations up to homotopy, we define a cochain complex that is canonically associated to any VB-groupoid. The cohomology of this complex is isomorphic to the groupoid cohomology with values in the corresponding representations up to homotopy. The classification of regular VB-groupoids leads to a new cohomological invariant associated to regular Lie groupoids.
Gracia-Saz Alfonso
Mehta Rajan Amit
No associations
LandOfFree
VB-groupoids and representation theory of Lie groupoids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with VB-groupoids and representation theory of Lie groupoids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and VB-groupoids and representation theory of Lie groupoids will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-184017