Handbook of Geometry and Topology of Singularities III
暫譯: 奇異性幾何與拓撲手冊 III
Cisneros-Molina, José Luis, Dũng Tráng, Lê, Seade, José
- 出版商: Springer
- 出版日期: 2023-06-08
- 售價: $11,710
- 貴賓價: 9.5 折 $11,125
- 語言: 英文
- 頁數: 802
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3030957624
- ISBN-13: 9783030957629
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商品描述
This is the third 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. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariski's equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom-Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more.
Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways.
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《奇異性幾何與拓撲手冊》第三卷，該系列旨在提供該主題的最新進展、邊界及其與其他研究領域的互動的易懂介紹。本卷包含十個章節，深入且易於閱讀地調查了奇異性理論的各個重要方面。其中一些主題補充了第一卷和第二卷中先前探討的內容，例如 Zariski 的等奇異性、孤立複雜曲面奇異性與三維流形理論之間的相互作用、分層 Morse 理論、可構造層、全純函數的非臨界層次的拓撲以及交集同調。其他章節則引入了新主題，例如映射的 Thom-Mather 理論、奇異多樣體的特徵類、混合 Hodge 結構、複分析多樣體中的殘差、鄰近循環和消失循環等。
奇異性在數學和科學中無處不在。奇異性理論與數學的其他部分進行著活躍的互動，充當一個熔爐，在這裡不同類型的數學問題相互作用，驚人的聯繫誕生，簡單的問題引發的想法在該主題的其他部分以及其他學科中引起共鳴。這本書由世界專家撰寫，各種貢獻涵蓋了經典材料和現代發展，涵蓋了廣泛的主題，這些主題在根本上彼此相連。
本書適合研究生和初學者，以及可以將其作為指南的專家。
作者簡介
Dũng Tráng Lê (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, carousels, among other topics.
José Seade (DPhil, University of Oxford 1980) is a full-time 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. In 2007 he was awarded the Ferran Sunyer i Ballaguer prize, and he was awarded the 2021 Solomon Lefschetz Medal by the Mathematical Council of the Americas.
作者簡介(中文翻譯)
何塞·路易斯·西斯內羅斯-莫利納（博士，華威大學 1999 年）是墨西哥國立自治大學數學研究所的全職研究員。他的研究興趣包括代數與微分拓撲、微分幾何和奇異性理論，特別專注於對於複數和實數解析映射的米爾諾纖維化的推廣。
鄧長樂（博士，巴黎大學 1969 年）是艾克斯-馬賽大學的名譽教授。之前他曾擔任巴黎第七大學（1975-1999）和馬賽大學的教授，並且是三里士國際理論物理中心數學部的負責人。他是現代奇異性理論的創始人之一，對於莫爾化、複數奇異性的拓撲、極點多樣體、旋轉木馬等主題做出了許多貢獻。
何塞·西德（博士，牛津大學 1980 年）是墨西哥國立自治大學數學研究所的全職研究員。他的研究集中在奇異多樣體的向量場指數和陳類的理論，並應用於葉狀結構以及米爾諾的解析映射纖維化定理。2007 年，他獲得了費蘭·蘇尼耶·巴拉格獎，並於 2021 年獲得美洲數學委員會頒發的所羅門·萊夫謝茨獎章。
