# flat connections in a sentence

- This shows the need to restrict to
*flat connections* with regular singularities in the Riemann Hilbert correspondence. *Flat connections* are determined entirely by holonomies around noncontractible cycles on the base " M ".- This natural
*flat connection* is a Gauss Manin connection " and can be described by the Picard Fuchs equation. - This equation corresponds to a
*flat connection* on the trivial algebraic line bundle over " A " 1. - A much more elementary theorem than the Riemann Hilbert correspondence states that
*flat connections* on holomorphic vector bundles are determined up to isomorphism by their monodromy. - It's difficult to find
*flat connections* in a sentence. - Since the functions " ce z " are defined on the whole affine line " A " 1, the monodromy of this
*flat connection* is trivial. - They can also be regarding as a natural extension of the Atiyah Bott symplectic structure on spaces of
*flat connections* on Riemann surfaces to the world of meromorphic geometry-a perspective pursued by Philip Boalch. - One of the driving forces for the study of Hamiltonian group action is its application to moduli spaces; for example, the moduli space of
*flat connections* . ( This article however focuses on finite-dimensional spaces .) - But this
*flat connection* is not isomorphic to the obvious flat connection on the trivial line bundle over " A " 1 ( as an algebraic vector bundle with flat connection ), because its solutions do not have moderate growth at ". - But this flat connection is not isomorphic to the obvious
*flat connection* on the trivial line bundle over " A " 1 ( as an algebraic vector bundle with flat connection ), because its solutions do not have moderate growth at ". - But this flat connection is not isomorphic to the obvious flat connection on the trivial line bundle over " A " 1 ( as an algebraic vector bundle with
*flat connection* ), because its solutions do not have moderate growth at ". - On the other hand, if we work with holomorphic ( rather than algebraic ) vector bundles with
*flat connection* on a noncompact complex manifold such as " A " 1 = "'C "', then the notion of regular singularities is not defined. - The condition of regular singularities means that locally constant sections of the bundle ( with respect to the
*flat connection* ) have moderate growth at points of " Y " X ", where " Y " is an algebraic compactification of " X ".