Bordism groups of fold maps
For a fixed codimension \(k>0\) denote by \(r\sum^0 +s\sum^{1,0}\) the multisingularity of a \(k\) codimensional mapping consisting of the transverse intersection of \(r\) regular points and \(s\) fold points. The authors consider sets of multisingularities of the form \(I=I_m=\{\sum^{1,0}\}\cup \{j\sum^0 :j\leq m\}\) for some \(m\geq 2\). The main result of this interesting paper presents an algorithmic way of computation for the \(\mathbb{Z}_2\)-dimension of the left-right bordism groups \(Bord _{I}(n)\). For \(I=I_2\) an explicit formula is given in Theorem 1. These results are directly connected to \textit{T. Ekholm, A. Szűcs} and \textit{T. Terpai} [Kyushu J. Math. 61, No. ~2, 395--414 (2007; Zbl 1156.57024)] and to \textit{A. Szűcs} [Acta Math. Acad. Sci. Hung. 27, 343--358 (1976; Zbl 0356.57024)], \textit{A. Szűcs} [Mat. Sb., N. Ser. 108(150), 433--456 (1979; Zbl 0412.57023)], \textit{A. Szűcs} [Osaka J. Math. 21, 71--80 (1984; Zbl 0553.57012)], \textit{A. Szűcs} [Math. Proc. Camb. Philos. Soc. 100, 331--346 (1986; Zbl 0625.57017)] and \textit{A. Szűcs} [Geom. Topol. 12, No. ~4, 2379--2452 (2008; Zbl 1210.57028)].
scientific article; zbMATH DE number 5857761
scientific article