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\centerline{\bf Characteristic Classes for Singularities of Linear Differential
Equations}

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\centerline{A. Levelt}
\centerline{Catholic University}
\centerline{Department of Mathematics}
\centerline{NL - 6525 Nijmegen, The Netherlands}
\centerline{Email: ahml@sci.kun.nl}

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The differential equations in question are homogeneous linear differential
equations (of any order) and systems of homogeneous linear differential
equations of order one. In both cases the coefficients belong to the field
K=k((x)) of formal Laurent series in x with finite pole order. These equations
are studied from the point of view of linear differential operators in finite
dimensional vector spaces over K. The results resemble those of the theory
of linear transformations in finite dimensional vector spaces, though the
proofs are quite different, because for differential operators their is no
(direct) way to define a characteristic polynomial. In his Ph.D. thesis
(Nijmegen, 1993) R. Sommeling constructed a new object, the characteristic
class of a differential operator, which has the properties which one might
expect. A somewhat simplified treatment will be presented as well as
remarks on computations.

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