Periodic Points of Maps on Infra-Nilmanifolds
- 발행기관 서강대학교 일반대학원
- 지도교수 이종범
- 발행년도 2010
- 학위수여년월 2010. 8
- 학위명 박사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/sogang/000000046155
- 본문언어 영어
초록/요약
This thesis is concerned with the study of periodic points of self-maps on infra-nilmanifolds. First, generalizing toral automorphisms on tori, we define (infra-)nil endomorphisms on (infra-)nilmanifolds and then we prove that every (infra-)nil endomorphism has dense eventually periodic points. Next, we focus on periodic points of self-maps on the Klein bottle, which is the well-known example of an infra-nilmanifold, but not a nilmanifold. We compute the homotopy invariants, the Lefschetz numbers and the Nielsen numbers, of all iterates of a self-map on the Klein bottle by using the averaging formulas for the Lefschetz numbers and the Nielsen numbers on infra-nilmanifolds. Finally, we provide a complete description of the formulas for the homotopy invariants, the two Nielsen type numbers NP_n(f) and NΦ_n(f) of a self-map f on the Klein bottle.
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