Sentence examples for flat connections from inspiring English sources

The adjective "flat" here is supposed to reflect the fact that these are the tangent structures to general flat connections.

This induces a symplectic structure for the moduli space of flat connections with boundary holonomies lying in prescribed conjugacy classes.

Moreover, under an additional geometrical hypothesis, we show that the transformationΦSestablishes an equivalence of categories between coherent DX-modules, modulo flat connections, and coherent DY-modules with regular singularities along an involutive manifoldV, modulo flat connections (hereVis determined by the geometry of the correspondence).

It would be fair to say that most of the constructions and results on Sabinin algebras mentioned in the previous section were the product of a quest for a Lie theory of flat connections.

On the tangent bundle ({T} G) there exists a canonical flat connection (nabla ).

The construction of the geodesic loop associated with a flat connection is due to Kikkawa [24] and Sabinin [49].

It can be seen that each flat connection on a neighbourhood of a point comes from a local loop, called the geodesic loop of the connection.

In the case of the lower reservoir there is a nearby access road, so only a short and flat connection to it is necessary.

For example, it is possible to produce a one-sided flat connection, which is not producible with any other joining technology.

From this construction it is clear that given a flat Sabinin algebra (mathfrak {l}) one can reconstruct, locally, the corresponding flat connection, and, hence, the infinitesimal loop, provided that the operations of (mathfrak {l}) define converging power series.

Indeed, there are two constructions of the tangent structure to a local (infinitesimal, formal) loop and both are based on the fact that there is a flat connection associated with a local loop, see the next section.