A Course on Holomorphic Discs

Geiges, Hansjörg, Zehmisch, Kai

A Course on Holomorphic Discs
  • 出版商: Birkhauser Boston
  • 出版日期: 2024-07-07
  • 售價: $2,330
  • 貴賓價: 9.5 折 $2,214
  • 語言: 英文
  • 頁數: 189
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031360664
  • ISBN-13: 9783031360664

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商品描述

This textbook, based on a one-semester course taught several times by the authors, provides a self-contained, comprehensive yet concise introduction to the theory of pseudoholomorphic curves. Gromov's nonsqueezing theorem in symplectic topology is taken as a motivating example, and a complete proof using pseudoholomorphic discs is presented. A sketch of the proof is discussed in the first chapter, with succeeding chapters guiding the reader through the details of the mathematical methods required to establish compactness, regularity, and transversality results. Concrete examples illustrate many of the more complicated concepts, and well over 100 exercises are distributed throughout the text. This approach helps the reader to gain a thorough understanding of the powerful analytical tools needed for the study of more advanced topics in symplectic topology.
This text can be used as the basis for a graduate course, and it is also immensely suitable for independentstudy. Prerequisites include complex analysis, differential topology, and basic linear functional analysis; no prior knowledge of symplectic geometry is assumed.
This book is also part of the Virtual Series on Symplectic Geometry.

商品描述(中文翻譯)

這本教科書基於作者多次教授的一學期課程，提供了一個自成體系、全面而簡潔的偽全曲線理論介紹。Gromov 在辛拓撲中的非擠壓定理被作為一個激勵範例，並提供了使用偽全圓盤的完整證明。第一章討論了證明的概要，隨後的章節引導讀者了解建立緊湊性、正則性和橫交性結果所需的數學方法的細節。具體的例子說明了許多較為複雜的概念，並在文本中分佈了超過 100 道練習題。這種方法幫助讀者深入理解研究辛拓撲中更高級主題所需的強大分析工具。

這本書可以作為研究生課程的基礎，也非常適合獨立學習。先修課程包括複變分析、微分拓撲和基本的線性泛函分析；不假設有辛幾何的先前知識。

這本書也是 辛幾何虛擬系列 的一部分。

作者簡介

Hansjörg Geiges, born in Basel in 1966, is Professor of Mathematics at the Universität zu Köln. He received his PhD from the University of Cambridge in 1992. Before moving to his current position in 2002, he taught at Stanford University, ETH Zürich, and the Universiteit Leiden. His other published books are An Introduction to Contact Topology and The Geometry of Celestial Mechanics.
Kai Zehmisch, born in Leipzig in 1975, is Professor of Mathematics at the Ruhr-Universitat Bochum. He obtained his doctorate at the Universität Leipzig in 2009, after having lived through the failure of the second socialist experiment on German soil, and was rewarded nonetheless with a book prize on 100 Jahre Mathematisches Seminar der Karl-Marx-Universität Leipzig. Previous to his current position, he taught at the Westfälische Wilhems-Universität Münster (as it was then called) and at the Justus-Liebig-Universität Giessen.

作者簡介(中文翻譯)

漢斯約爾格·蓋格斯（Hansjörg Geiges），1966年出生於巴塞爾，現任科隆大學（Universität zu Köln）數學教授。他於1992年在劍橋大學（University of Cambridge）獲得博士學位。在2002年擔任目前職位之前，他曾在斯坦福大學（Stanford University）、蘇黎世聯邦理工學院（ETH Zürich）和萊頓大學（Universiteit Leiden）任教。他的其他出版書籍包括《接觸拓撲學導論》（An Introduction to Contact Topology）和《天體力學的幾何學》（The Geometry of Celestial Mechanics）。

凱·澤米施（Kai Zehmisch），1975年出生於萊比錫，現任魯爾大學波鴻（Ruhr-Universität Bochum）數學教授。他於2009年在萊比錫大學（Universität Leipzig）獲得博士學位，期間經歷了德國土地上第二次社會主義實驗的失敗，然而仍然因其著作《卡爾·馬克斯·萊比錫大學數學研討會100年》（100 Jahre Mathematisches Seminar der Karl-Marx-Universität Leipzig）獲得了書籍獎。在擔任目前職位之前，他曾在西法倫威爾斯大學明斯特（當時稱為Westfälische Wilhelms-Universität Münster）和尤斯圖斯·利比希大學吉森（Justus-Liebig-Universität Giessen）任教。

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