The Graded Cobordism Group of Codimension-One Immersions

Codimension one immersions and the Kervaire invariant one problem

Imbeddings, Immersions, and Cobordism of Differentiable Manifolds

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...

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...

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.