Handbook of Geometry and Topology of Singularities V: Foliations

Cano, Felipe, Cisneros-Molina, José Luis, Dũng Tráng, Lê

Handbook of Geometry and Topology of Singularities V: Foliations
  • 出版商: Springer
  • 出版日期: 2024-06-06
  • 售價: $8,330
  • 貴賓價: 9.5 折 $7,914
  • 語言: 英文
  • 頁數: 510
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031524802
  • ISBN-13: 9783031524806

    • 海外代購書籍(需單獨結帳)

商品描述

This is the fifth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. Singularities are ubiquitous in mathematics and science in general, and singularity theory is a crucible where different types of mathematical problems converge, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects.

This Volume V focuses on singular holomorphic foliations, which is a multidisciplinary field and a whole area of mathematics in itself. Singular foliations arise, for instance, by considering:

  1. The fibers of a smooth map between differentiable manifolds, with singularities at the critical points.
  2. The integral lines of a vector field, or the action of a Lie group on a manifold. The singularities are the orbits with special isotropy.
  3. The kernel of appropriate 1-forms. The singularities are the zeros of the form.
  4. Open books, which naturally appear in singularity theory as foliations with singular set the binding.

These important examples highlight the deep connections between foliations and singularity theory. This volume, like its companion Volume VI, also focused on foliations, consists of nine chapters, authored by world experts, which provide in-depth and reader-friendly introductions to some of the foundational aspects of the theory. These introductions also give insights into important lines of further research. The volume starts with a foreword by one of the current world leaders in the theory of complex foliations.

The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

商品描述(中文翻譯)

這是《奇異點幾何與拓撲手冊》的第五卷，該系列旨在提供對該主題的最新狀態、前沿和與其他研究領域的交互作用的易於理解的描述。奇異點在數學和科學中無處不在，奇異點理論是一個不同類型的數學問題匯聚的地方，令人驚訝的聯繫產生，簡單的問題引發的思想在該主題的其他部分和其他學科中產生共鳴。

第五卷專注於奇異全純葉，這是一個多學科領域，也是數學的一個完整領域。奇異葉的出現，例如通過考慮：

1. 不同可微流形之間的平滑映射的纖維，在臨界點處有奇異點。
2. 向量場的積分線，或李群對流形的作用。奇異點是具有特殊等度的軌道。
3. 適當的1-形式的核。奇異點是形式的零點。
4. 在奇異點理論中自然出現的葉，其奇異集是綁定。

這些重要的例子突顯了葉和奇異點理論之間的深刻聯繫。這卷，就像它的同伴第六卷一樣，也專注於葉，由世界專家撰寫的九章提供了對該理論一些基礎方面的深入且易於理解的介紹。這些介紹還提供了進一步研究的重要線索。該卷以當前複雜葉理論領域的世界領導者之一的序言開始。

本書針對研究生和新手，以及專家可以將其用作指南。

作者簡介

Felipe Cano Torres (PhD Universidad de Valladolid, Spain, 1983) is a researcher at Universidad de Valladolid. His research is on holomorphic foliations, particularly on reduction of singularities and applications to dynamical systems. Director of research of several international networks with European fundings. Co-founder and current subdirector of the CTRI, a center in Tordesillas, Spain, focusing on the relations between the University of Valladolid and Iberoamerica.

José Luis Cisneros-Molina (PhD, University of Warwick 1999) is a researcher at the Mathematics Institute of the National Autonomous University of Mexico. His research interests are in Algebraic and Differential Topology, Differential Geometry and Singularity Theory, with a particular focus on generalizations of Milnor Fibrations for complex and real analytic maps.

Lê Dũng Tráng (PhD, University of Paris 1969) is an Emeritus Professor at Aix-Marseille University. Previously he was Professor at the Universities of Paris VII (1975-1999) and Marseille, and was head of Mathematics at the ICTP at Trieste. One of the founders of modern Singularity Theory, he has made numerous contributions to morsification, the topology of complex singularities, polar varieties, and carousels, among other topics.

José Seade (DPhil, University of Oxford 1980) is a researcher at the Mathematics Institute of the National Autonomous University of Mexico. His research is in the theory of indices of vector fields and Chern classes for singular varieties, with applications to foliations, and Milnor's fibration theorem for analytic maps. He was awarded the 2021 Solomon Lefschetz Medal by the Mathematical Council of the Americas. He is currently President of the Mexican Academy of Sciences.

作者簡介(中文翻譯)

Felipe Cano Torres（西班牙瓦拉多利德大學，1983年獲得博士學位）是瓦拉多利德大學的研究員。他的研究領域是全純葉片，尤其是奇異點的減少和應用於動力系統。他是幾個國際研究網絡的研究主任，並獲得歐洲資助。他是西班牙托德西利亞斯的CTRI中心的聯合創始人和現任副主任，該中心專注於瓦拉多利德大學與伊比利亞美洲之間的關係。

José Luis Cisneros-Molina（華威大學，1999年獲得博士學位）是墨西哥國立自治大學數學研究所的研究員。他的研究興趣包括代數和微分拓撲、微分幾何和奇異點理論，尤其關注複解析和實解析映射的Milnor纖維化的推廣。

Lê Dũng Tráng（巴黎大學，1969年獲得博士學位）是艾克斯-馬賽大學的名譽教授。他曾任教於巴黎第七大學（1975-1999年）和馬賽大學，並擔任過國際理論物理中心（ICTP）的數學主任。作為現代奇異點理論的創始人之一，他在奇異化、複雜奇異點的拓撲、極性變量和旋轉木馬等領域做出了許多貢獻。

José Seade（牛津大學，1980年獲得博士學位）是墨西哥國立自治大學數學研究所的研究員。他的研究領域是向量場的指數理論和奇異變量的Chern類理論，並應用於葉片和Milnor的解析映射纖維化定理。他獲得了2021年美洲數學理事會頒發的Solomon Lefschetz獎章。他目前擔任墨西哥科學院院長。

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