COMPUTATION OF THE NIELSEN TYPE NUMBERS FOR MAPS ON THE KLEIN BOTTLE

Title & Authors
COMPUTATION OF THE NIELSEN TYPE NUMBERS FOR MAPS ON THE KLEIN BOTTLE
Kim, Hyun-Jung; Lee, Jong-Bum; Yoo, Won-Sok;

Abstract
Let f : M $\small{{\rightarrow}}$ 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 $\small{NP_n(f)}$ and $\small{N{\Phi}_{n}(f)\;of\;f^{n}}$.
Keywords
Klein bottle;Nielsen type numbers;weakly Jiang maps;
Language
English
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