See also

- Research papers (full list)
- Hamiltonian abstracts
- Other abstracts

In

- We consider corank-1 map-germs from

- We show how the path formulation of bifurcation theory
can be made to work, and that it is (essentially) equivalent
to the usual parametrized contact equivalence of Golubitsky
and Schaeffer. If there is more than one bifurcation
parameter present in the problem, it seems clear that the path
approach is preferable to the distinguished parameter
approach, since the tangent spaces in question are easier to
compute. [ Paper (218K)]

- A result due to Jim Damon relates the
A

The extension of Damon's theorem is used to provide an extension (again to cases where the source is an icis) of a result of Damon and Mond relating the discriminant Milnor number of a map to its left-right-codimension. [ Paper (222K)]

- The purpose of this expository article is to describe in
an elementary and homogeneous manner, the relationship between
the geometric and algebraic multiplicities of isolated
critical points of holomorphic functions. In particular, I am
interested in the setting where the function is invariant
under some group action. The emphasis is on functions
invariant under actions of finite groups as very little is
known if the group is not finite.

Most of the results described here are already explicitly in the literature; the only small extension is to functions that are not invariant, but

- Consider a function on

- It is shown that (in the nice dimensions) if a stable map is restricted to a generic
submanifold of the source manifold, then the reulting map will also be stable. At the same
time, the analgous result for versal unfoldings is proved.
A few examples of applications to the extrinsic geometry of submanifolds are discussed.

Paper (via DOI)

- Let C be a real analytic curve in

In the case that C is a complete intersection in some neighbourhood of p (i.e. it is given locally by n-1 equations) then there is a solution to this problem due to K. Aoki, T. Fukuda and T. Nishimura. In this paper, we give a general solution to the problem.

This solution uses meromorphic differential forms on the complexification of the curve, and properties of the module of Rosenlicht differentials, defined in terms of residues. A 1-form on a real curve defines an orientation, and the method allows one to find the number of branches counted with orientation for any given 1-form; particular choices of the form will then give the total number of branches.

Paper (via DOI)

- The higher-order local extrinsic differential geometry of surfaces in 3-space is described in terms of the contact between the surface and all possible circles.

Paper (via Project Euclid)

- We make use of singularity theory to define the contact between submanifolds of a manifold, whether or not the submanifolds are of complementary dimension.

Paper (via DOI)

James Montaldi