synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
In the context of T-duality and in particular of differential T-duality one considers (as discussed in detail there) fiber products of two torus-fiber bundles together with a circle 2-bundle on this, (with connection).
In some disguise, this has been called -geometry (Baraglia). The T-duality interpretation is made explicit in Bouwknegt
Here “” refers to the special orthogonal group of the form , which appears as the structure group of a generalized tangent bundle tensored with a line bundle (the Poincare line bundle of the T-duality correspondence).
We give the interpretation of -geometry in higher differential geometry.
For modulating two circle principal bundles with conection, a differential T-duality structure is a choice of trivialization of their cup product class. From this we get the pasting diagram of homotopy pullbacks of smooth -stacks
Here is the morphism that modulates the circle 2-bundle on the fiber product of the two circle bundles.
(…)
The term -geometry was introduced in
A review is in
The relation to T-duality is made clear around slide 80 of
A discussion of the higher Lie theoretic aspects is in
Last revised on March 17, 2018 at 12:44:42. See the history of this page for a list of all contributions to it.