Posted on Categories:Low Dimensional Topology, 低维拓扑, 数学代写

# 数学代写|低维拓扑代写Low Dimensional Topology代考|MATH282A Lifting a permutation movie to a braid movie

avatest™

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 数学代写|低维拓扑代写Low Dimensional Topology代考|Lifting a permutation movie to a braid movie

A braid chart of degree $n$ is a permutation chart in which orientations on the edges have been chosen so that white vertices and crossings are of the form indicated in the figure. Thus there are three incoming and three outgoing edges that alternate $i, i \pm 1, i, i \pm 1, i, i \pm 1$ in cyclic order. Similarly, at a crossing the edges with labels $i$ and the edges with labels $j$ are oriented consistently $(|i-j|>1)$ as indicate in Fig. 14. In this case, we say that there is a flow though the white vertex or the crossing. If a permutation chart can be consistently oriented to create a braid chart, then the permutation movie can be lifted to a braid movie. Specifically, right pointing edges with label $i$ correspond to braid generators $\sigma_i$, and left pointing edges with label $i$ correspond to $\sigma_i^{-1}$.

Let $\Gamma_n$ denote a degree $n$ permutation chart. If there is a consistent orientation on the edges of $\Gamma_n$, then the opposite orientation will also be consistent; we let $\Gamma_n^{\pm}$denote the resulting braid charts. As before, let $M^2(\Gamma)$ denote the $n$-fold irregular simple branched cover of $D^2$ that is associated to the chart $\Gamma=\Gamma_n$, and let $\hat{M}(\Gamma)$ denote its extension to the 2 -sphere.

Theorem 3.5. If $\Gamma_n^{\pm}$is a braid chart, then there is an embedding, $\tilde{F}: \hat{M}(\Gamma) \rightarrow S^2 \times[0,1] \times[0,1]$ of the $n$-fold irregular simple branched cover $F: \hat{M}(\Gamma) \rightarrow S^2$ such that the composition $p \circ \tilde{F}$ agrees with the covering map $F$ where $p: S^2 \times[0,1] \times[0,1] \rightarrow S^2$ is the projection onto the first factor. In this way the covering $F$ has a folded embedding.

Proof. The lifting of each permutation to a braid induces an embedding of the surface $\hat{M}$ into $S^2 \times[0,1] \times[0,1]$. The projection to the first two factors $S^2 \times[0,1]$ induces the generic map of Proposition 3.4.

## 数学代写|低维拓扑代写Low Dimensional Topology代考|A partial lifting

It is possible that a given chart cannot be oriented consistently so that all white vertices have a flow. A semi-oriented chart is a permutation chart $\Gamma^*$ that includes a fourth type of vertex which is bivalent, and the chart is oriented such that (1) each bivalent vertex is either a source or a sink and (2) each white vertex and each crossing has a flow. At a source vertex the two emanating edges have the same label and point away from the vertex. At a $\operatorname{sink}$ the edges point towards the vertex.
Lemma 3.6. Any permutation chart can be semi-oriented.
Proof. Locally orient the edges so that there is a flow through all white vertices and all crossings. If there is an edge whose endpoints are either white vertices or crossings such that the local orientations do not match, then introduce a source or sink. Do the same for all such edges.

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。