# Cobordism classes of maps and covers for spheres

## TL;DR

This paper proves that for dimensions m>n, all cobordism classes of maps from m-spheres to n-spheres are trivial, with implications for understanding sphere covers.

## Contribution

It establishes the triviality of cobordism classes of sphere maps for m>n and explores applications to sphere covers.

## Key findings

- Cobordism classes of maps from m-sphere to n-sphere are trivial for m>n.
- Results have applications in the theory of covers for spheres.
- Provides a new perspective on cobordism homotopy groups of spheres.

## Abstract

In this paper we show that for m>n the set of cobordism classes of maps from m-sphere to n-sphere is trivial. The determination of the cobordism homotopy groups of spheres admits applications to the covers for spheres.