Bounds on coincidence indices on non-orientable surfaces (Q2483735)

The author presents some results about bounds for coincidence indices of Nielsen coincidence classes for pairs of maps between some non-orientable surfaces, when the degrees of the two maps involved are given. Such results generalize the similar consideration for maps on orientable surfaces, which were given by \textit{D. Gonçalves} and \textit{B. Jiang} [Topology Appl. 116, No. 1, 73--89 (2001; Zbl 0987.55004)]. Here, the degrees are absolute ones given by \textit{Robert F. Brown} and \textit{H. Schirmer} [Pac. J. Math. 198, No. 1, 49--80 (2001; Zbl 1049.55001)], and the coincidence indices are semi-indices defined by \textit{R. Dobrenko} and \textit{J. Jezierski} [Rocky Mt. J. Math. 23, No. 1, 67--85 (1993; Zbl 0787.55003)]. The non-orientable surfaces concerned here are mainly connected sums of \(n\) tori with a Klein bottle, written by \(K_n\). It is shown that (i) for pairs of maps from the Klein bottle to a surface \(K_n\), the coincidence class index is bounded; (ii) for pairs of maps from \(K_n\) (\(n\neq 0\)) to the Klein bottle, the coincidence class index is unbounded. Other boundedness results for coincidence indices are given.