In the geometric version of the Langlands correspondence, irregular singular
point connections play the role of Galois representations with wild
ramification. In this paper, we develop a geometric theory of fundamental
strata to study irregular singular connections on the projective line.
Fundamental strata were originally used to classify cuspidal representations of
the general linear group over a local field. In the geometric setting,
fundamental strata play the role of the leading term of a connection. We
introduce the concept of a regular stratum, which allows us to generalize the
condition that a connection has regular semisimple leading term to connections
with non-integer slope. Finally, we construct a symplectic moduli space of
meromorphic connections on the projective line that contain a regular stratum
at each singular point.Comment: 53 pages. A new section (Section 4.4) has been added making precise
the relationship between formal types and isomorphism classes of formal
connections. Significant revisions and additions have also been made to
Sections 3.1 and 4.3 and the introduction to Section
