• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.205-211
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• 1996

Throughout this paper, we will work in the category of compact connected manifolds and continuous maps. If $X_1, X_2$ are manifolds, $f, g: X_1 \to X_2$ are maps, then a point $x \in X_1$ is a coincidence of f and g iff f(x) = g(x) ; the set of all such points is denoted by Coin(f,g).

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1483-1503
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• 2008

Let f : M ${\rightarrow}$ M be a self-map on the Klein bottle M. We compute the Lefschetz number and the Nielsen number of f by using the infra-nilmanifold structure of the Klein bottle and the averaging formulas for the Lefschetz numbers and the Nielsen numbers of maps on infra-nilmanifolds. For each positive integer n, we provide an explicit algorithm for a complete computation of the Nielsen type numbers $NP_n(f)$ and $N{\Phi}_{n}(f)\;of\;f^{n}$.