Groups of classes of pseudo-homotopic singular links. I

V. M. Nezhinskii

Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 9, Tome 168 (1988), pp. 114-124

Résumé

By a singular link of type $(p_1,p_2)$ in $S^n$ we mean a pair of continuous mappings $S^{p_1}\to S^n$, $S^{p_2}\to S^n$ with disjoint images. In the paper the concept of the pseudohomotopy of singular links is defined, similar to the concept of concordance of classical links, and it is proved that for $n>p_2+2$ the set of the classes of pseudohomotopic singular links of type $(p_1,p_2)$ in $S^n$ forms an Abelian group with respect to a componentwise connected summation. This group has been obtained in case $n\geq2p_2+1-\max\{n-p_1-2,0\}$.