ON MULTIPLE POINTS OF CODIMENSION ONE IMMERSIONS OF EVEN-DIMENSIONAL MANIFOLDS

Codimension one immersions and the Kervaire invariant one problem

Cobordism class of multiple points of immersions

Using generating functions, we derive a multiple point formula for every generic immersion f : M # N between even dimensional oriented manifolds. This produces explicit formulas for the signature and Pontrjagin numbers of the multiple point manifolds. The formula takes a particular simple form in many special cases, e.g. when f is nullhomotopic we recover Szűcs’s formula in [3]. It also include...

Isometric Immersions into 3-dimensional Homogeneous Manifolds

We give a necessary and sufficient condition for a 2-dimensional Riemannian manifold to be locally isometrically immersed into a 3-dimensional homogeneous manifold with a 4-dimensional isometry group. The condition is expressed in terms of the metric, the second fundamental form, and data arising from an ambient Killing field. This class of 3-manifolds includes in particular the Berger spheres,...

Immersions of manifolds.

This paper outlines a proof of the conjecture that every compact, differentiable, n-dimensional manifold immerses in Euclidean space of dimension 2n - alpha(n), where alpha(n) is the number of ones in the dyadic expansion of n.

Directed Immersions of Closed Manifolds

Given any finite subset X of the sphere S, n ≥ 2, which includes no pairs of antipodal points, we explicitly construct smoothly immersed closed orientable hypersurfaces in Euclidean space R whose Gauss map misses X. In particular, this answers a question of M. Gromov.