Cobordisms of maps without prescribed singularities
Abstract
Let $N$ and $P$ be smooth closed manifolds of dimensions $n$ and $p$ respectively. Given a Thom-Boardman symbol $I$, a smooth map $f:N\to P$ is called an $\Omega^{I}$-regular map if and only if the Thom-Boardman symbol of each singular point of $f$ is not greater than $I$ in the lexicographic order. We will represent the group of all cobordism classes of $\Omega^{I}$-regular maps of $n$-dimensional closed manifolds into $P$ in terms of certain stable homotopy groups. As an application we will study the relationship among the stable homotopy groups of spheres, the above cobordism group and higher singularities.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- December 2004
- DOI:
- arXiv:
- arXiv:math/0412234
- Bibcode:
- 2004math.....12234A
- Keywords:
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- Geometric Topology;
- 57R45;
- 57R90
- E-Print:
- 26pages