Submersions and immersions with codimension one or two

Codimension one immersions and the Kervaire invariant one problem

Geometric Formulas for Smale Invariants of Codimension Two Immersions

We give three formulas expressing the Smale invariant of an immersion f of a (4k− 1)-sphere into (4k + 1)-space. The terms of the formulas are geometric characteristics of any generic smooth map g of any oriented 4k-dimensional manifold, where g restricted to the boundary is an immersion regularly homotopic to f in (6k − 1)-space. The formulas imply that if f and g are two non-regularly homotop...

On the Construction of Codimension-two Minimal Immersions of Exotic Spheres

Codimension One Symplectic Foliations

We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.

Codimension One Branes

We study codimension one branes, i.e. p-branes in (p + 2)-dimensions, in the superembedding approach for the cases where the worldvolume superspace is embedded in a minimal target superspace with half supersymmetry breaking. This singles out the cases p = 1, 2, 3, 5, 9. For p = 3, 5, 9 the superembedding geometry naturally involves a fundamental super 2-form potential on the worldvolume whose g...