bisection of a Lie groupoid
∞-Lie theory (higher geometry)
Formal Lie groupoids
Bisections of Lie groupoids
Let be a Lie groupoid.
A bisection of is a smooth function such that
is a section of ;
is a diffeomorphism.
Bisections naturally form a group under pointwise composition in , the group of bisections of the Lie groupoid.
Let Smooth∞Grpd. Let be equipped with an atlas, hence with an effective epimorphism out of a 0-truncated object.
We may regard this atlas as an object in the slice (∞,1)-topos
The smooth ∞-group of bisections of is its automorphism ∞-group
Relation to Lie-Rinehart algebras
For a Lie groupoid with atlas as above, write for the Lie algebra of the group of bisections. Then is the Lie-Rinehart algebra corresponding to the Lie algebroid of the Lie groupoid.
Relation to Atiyah groupoids
for the moment see at Atiyah groupoid and higher Atiyah groupoid.
Revised on December 22, 2015 11:25:12
by Urs Schreiber