法向交叉浸入、配边与翻转

Cobordism of immersions of surfaces in non-orientable 3-manifolds

Some properties of non-orientable 3-manifolds are shown. The semi-group of cobordism of immersions of surfaces in such manifolds is computed and proven actually to be a group. Explicit invariants are provided.

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 defined by the author in his earlier works.

投影浸入的配边群上的计算

Computations on cobordism groups of projected immersions

本文通过 Szűcs 和 Terpai 的分类空间构造推广 Salomonsen 正合序列，研究具有指定奇点的超平面投影浸入的配边群，并在小余维和大余维情形下给出计算结果。

The graded cobordism group of codimension-one immersions

The cobordism group $N(M^n)$ of codimension-one immersions in the $n$-manifold $M^n$ has a natural filtration induced by any cellular decomposition. The problem addressed in this paper is the explicit computation of the graded group $gr^*N(M^n)$. We introduce some new invariants for immersions enlightening the Atiyah-Hirzebruch spectral sequence associated to $N(M)$, which are of combinatorial-geometric nature. Explicit computations are developed for $n\leq7$, and the group structure is also investigated for orientable 4-manifolds.

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 this 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 of the infinite dimensional projective space. By using geometric invariants defined in the author's earlier works, we also describe the natural map of the simple fold cobordism group to the fold cobordism group by na…

Fold maps, framed immersions and smooth structures

For each integer q>0 there is a cohomology theory such that the zero cohomology group of a manifold N of dimension n is a certain group of cobordism classes of proper fold maps of manifolds of dimension n+q into N. We prove a splitting theorem for the spectrum representing the cohomology theory of fold maps. For even q, the splitting theorem implies that the cobordism group of fold maps to a manifold N is a sum of q/2 cobordism groups of framed immersions to N and a group related to diffeomorphism groups of manifolds of dimension q+1. Similarly, in the case of odd q, the cobordism group of fol…