Analogues of the Atiyah--Wall exact sequences for cobordism groups of singular maps

Abstract

Classical results of Rohlin, Dold, Wall and Atiyah yield two exact sequences that connect the oriented and unoriented (abstract) cobordism groups ${\Omega }_n$ and ${\mathfrak{N}}_n$. In this paper we present analogous exact sequences connecting the oriented and unoriented cobordism groups of maps with prescribed singularities. This gives positive answer to a fifteen-year-old question posed by Szűcs and has interesting consequences even in the case of cobordisms of immersions.

arXiv comment51 pages, 2 figures