arXiv 2201.090142022-01math.ATmath.GT

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

András Csépai

备注：: 51 pages, 2 figures

英文摘要：

Classical results of Rohlin, Dold, Wall and Atiyah yield two exact sequences that connect the oriented and unoriented (abstract) cobordism groups $Ω_n$ 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.

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