Fixed points of surface diffeomorphisms.
Fixed points of surface diffeomorphisms.
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DOI：
10.2140/pjm.1993.160.67
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发表时间：
1993-09
影响因子：
0.6
通讯作者：
Boju Jiang;J. Guo
中科院分区：
文献类型：
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作者：
Boju Jiang;J. Guo
我们给出了以下定理的完整证明，该定理是 Jakob Nielsen 对于闭向曲面所猜想的。定理。令 f: M → M 为紧致曲面的同胚。当 M 闭合时，f 是具有 N(f) 个不动点的微分同胚的同位素，其中 N(f) 是其尼尔森数。当M有边界时，N(f)应替换为Schirmer定义的相对尼尔森数N(f; M, ∂M)。另一个结果是不等式 |L(f) − χ(M)| < N(f) − χ(M)，当 χ(M) < 0 时，其中 L(f) 是莱夫谢茨数，χ(M) 是欧拉特征
We give a complete proof of the following theorem which was conjectured by Jakob Nielsen for closed oriented surfaces. Theorem. Let f: M → M be a homeomorphism of a compact surface. When M is closed, then f is isotopic to a diffeomorphism with N(f) fixed points, where N(f) is its Nielsen number. When M has boundary, N(f) should be replaced by the relative Nielsen number N(f; M, ∂M) defined by Schirmer. Another result is the inequality |L(f) − χ(M)| < N(f) − χ(M) when χ(M) < 0, where L(f) is the Lefschetz number and χ(M) is the Euler characteristic