Cobordism class of multiple points of immersions

Fold Maps and Immersions from the Viewpoint of Cobordism

We obtain complete geometric invariants of cobordism classes of oriented simple fold maps of (n+ 1)-dimensional manifolds into an n-dimensional manifold N in terms of immersions with prescribed normal bundles. We compute that for N = R the cobordism group of simple fold maps is isomorphic to the direct sum of the (n−1)th stable homotopy group of spheres and the (n − 1)th stable homotopy group o...

Fold Maps, Framed Immersions and Smooth Structures

We show that the cobordism group of fold maps of even non-positive codimension q into a manifold N is a sum of q/2 cobordism groups of framed immersions into N and a group related to diffeomorphism groups of manifolds of dimension q + 1. In the case of maps of odd non-positive codimension q, we show that the cobordism groups of fold maps split off (q − 1)/2 cobordism groups of framed immersions.

Multiple point of self-transverse immesions of certain manifolds

In this paper we will determine the multiple point manifolds of certain self-transverse immersions in Euclidean spaces. Following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to Dold manifold $V^5$ or a boundary. We will show there is an immersion of $S^7times P^2$ in $mathbb{R}^{1...

Imbeddings, Immersions, and Cobordism of Differentiable Manifolds

Cobordism of Fold Maps, Stably Framed Manifolds and Immersions

We give complete geometric invariants of cobordisms of fold maps with oriented singular set and cobordisms of even codimensional fold maps. These invariants are given in terms of cobordisms of stably framed manifolds and cobordisms of immersions with prescribed normal bundles.