During the academic year 1974-75, the Department of Pure Mathematics in the University of
Liverpool held a seminar on the topological stability of smooth mappings. The main …

We show that the Deligne {Mumford compactification of the moduli space of smooth complex
curves of genus g admits a smooth Galois covering whose general point classifies curves …

The Knizhnik-Zamolodchikov equations were originally defined in terms of a local system
associated to tuples of finite dimensional irreducible representations of SU₂, but were soon …

Ideally (returning to the general situation) one seeks stratifications for which the local
topological type of'the pair (M, v) is constant on each stratum. From this point of view the …

We prove the assertion of the title. This implies that the cohomological dimension of Mg is≤
g− 2 for quasi-coherent sheaves (this amplifies Diaz’s theorem which says that Mg has no …

Throughout this chapter N and P are fixed manifolds and their dilnensions are denoted by
nand p respectively. § l Multi-transversality In the next sections we will encounter the following …

The mathematics described here arises from the study of smooth of mappings, and in particular
the associated local theory. For mappings, smooth stability is easily defined: a mapping …

A number of compactifications familiar in complex-analytic geometry, in particular the Baily–Borel
compactification and its toroidal variants, as well as the Deligne–Mumford …

36 § l This chapter is concerned with the construction of continuous flows on stratified sets.
Since strata are smooth manifolds we can clearly obtain a smooth flow on each stratum of a …