曲面基本群的无限表示

Pub Date : 2023-03-01 DOI:10.32917/h2022001

Ryoma Kobayashi

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引用次数: 0

摘要

对于任意有限型连通曲面S，我们给出了S的基群π1(S，*)的无限表示，π1(S，*)基于一个内部点*∈S，其生成点用简单环表示。当S不可定向时，我们也给出了π1(S，*)子群的无限表示，π1(S，*)子群是由正则邻域为环空的简单环所表示的。

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Inﬁnite presentations for fundamental groups of surfaces

For any ﬁnite type connected surface S, we give an inﬁnite presentation of the fundamental group π1(S,*) of S based at an interior point *∈S whose generators are represented by simple loops. When S is non-orientable, we also give an inﬁnite presentation of the subgroup of π1(S,*) generated by elements which are represented by simple loops whose regular neighborhoods are annuli.

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