曲面上Z_{p}^{m}作用的拓扑分类
几何拓扑
2007-05-23 v1 代数几何
摘要
设S ~ \widetilde{S} S g g g G G G Z p m \mathbf{Z}_{p}^{m} Z p m p p p G G G S S S ( S ~ , f ) (\widetilde{S},f) ( S , f ) f f f G G G S ~ \widetilde{S} S ( S ~ , f ) (\widetilde{S},f) ( S , f ) ( S ′ ~ , f ′ ) (\widetilde{S^{\prime}},f^{\prime}) ( S ′ , f ′ ) ψ ~ : S ~ → S ~ ′ \widetilde{\psi}:\widetilde{S}\to \widetilde{S}^{\prime} ψ : S → S ′ S ~ \widetilde{S} S S ~ ′ \widetilde{S}^{\prime} S ′ h ∈ G h\in G h ∈ G f ′ ( h ) = ψ ~ ∘ f ( h ) ∘ ψ ~ − 1 f^{\prime}(h)=\widetilde{\psi}\circ f(h)\circ \widetilde{\psi}^{-1} f ′ ( h ) = ψ ∘ f ( h ) ∘ ψ − 1 α ∈ A u t ( G ) \alpha \in Aut(G) α ∈ A u t ( G ) f ′ ∘ α ( h ) = ψ ~ ∘ f ( h ) ∘ ψ ~ − 1 f^{\prime}\circ \alpha (h)=\widetilde{\psi}\circ f(h)\circ \widetilde{\psi}^{-1} f ′ ∘ α ( h ) = ψ ∘ f ( h ) ∘ ψ − 1 Z p m \mathbf{Z}_{p}^{m} Z p m Z p m \mathbf{Z}_{p}^{m} Z p m G G G g g g k k k k ≤ m − n k\leq m-n k ≤ m − n k = ( m − n ) \func m o d 2 k=(m-n)\func{mod}2 k = ( m − n ) \func m o d 2 g ≥ 1 / 2 ( m − n + k ) g\geq {1/2}(m-n+k) g ≥ 1/2 ( m − n + k ) A u t ( G ) Aut(G) A u t ( G ) r r r [ C 1 , . . . , C r ] [C_{1},...,C_{r}] [ C 1 , ... , C r ] Z p n \mathbf{Z}_{p}^{n} Z p n ∑ 1 r C i = 0 \sum_{1}^{r}C_{i}=0 ∑ 1 r C i = 0 Z p m \mathbf{Z}_{p}^{m} Z p m
引用
@article{arxiv.math/0011249,
title = {Topological classification of Z_{p}^{m} actions on surfaces},
author = {Antonio F. Costa and Sergei M. Natanzon},
journal= {arXiv preprint arXiv:math/0011249},
year = {2007}
}