分段引理

The Plaid Model Pub Date : 2019-02-19 DOI:10.2307/j.ctv5rf6tz.13

R. Schwartz

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摘要

本章包含分段引理的陈述和证明。它固定了一个参数a = p/q，并设置p = 2A/(1 + a)，并延续了第8章的符号。本章组织如下。第9.2节解释了锚点的存在和形象。第9.3节解释了如何将第8.4节中的分类映射重新解释为定义在r3的某个子集上的映射。引理9.4的技术性结果将对本章的计算有用。第9.4节和第9.5节分别讨论了分段引理的垂直和水平情况。

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The Segment Lemma

This chapter contains the statement and proof of the Segment Lemma. It fixes a parameter A = p/q and set P = 2A/(1 + A) and continues the notation from Chapter 8. The chapter is organized as follows. Section 9.2 explains the existence and image of the anchor point. Section 9.3 explains how to reinterpret the classifying map from Section 8.4 as a map defined on a certain subset of R 3. The technical result, Lemma 9.4, will be useful for the computations in this chapter. Section 9.4 and 9.5 treats the vertical and horizontal cases of the Segment Lemma, respectively.

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The Plaid Model

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