For an explicit mapping $S^m\to S^6$ for $m<12$, how can we understand whether it is homotopy zero?

50 Views Asked by At

In my work I have mappings from $S^m$ to $S^6$, where $m\leq 11$. People know the homotopy group of these mappings. However, is there some algorithm that helps to recognize when mappings (we can assume that the mappings are simplicial) are homotopic to each other? I would be grateful for links.