Computation of the Nielsen type numbers for maps on the Klein bottle
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Let f : M → 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 infranilmanifolds. For each positive integer n, we provide an explicit algorithm for a complete computation of the Nielsen type numbers NPn(f) and NΦn(f) of fn.
Abstract
Let f : M → 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 infranilmanifolds. For each positive integer n, we provide an explicit algorithm for a complete computation of the Nielsen type numbers NPn(f) and NΦn(f) of fn.
참고문헌 (13)
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