曲面上的对合

Pub Date : 2019-05-14 DOI:10.1007/s40062-019-00236-1

Daniel Dugger

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引用次数: 16

摘要

我们用等变手术对闭合表面上的所有对合进行分类，直到同构。关于这个问题的研究是经典的，可以追溯到19世纪，直到20世纪90年代才出现了一个完整的分类。在本文中，我们给出了一种不同的分类方法，使用代数拓扑学家更容易理解的技术以及一个新的不变量(我们称之为double-Dickson不变量)来区分“困难”情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Involutions on surfaces

We use equivariant surgery to classify all involutions on closed surfaces, up to isomorphism. Work on this problem is classical, dating back to the nineteenth century, with a complete classification finally appearing in the 1990s. In this paper we give a different approach to the classification, using techniques that are more accessible to algebraic topologists as well as a new invariant (which we call the double-Dickson invariant) for distinguishing the “hard” cases.

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