Singularities and Low Dimensional Topology
暫譯: 奇異性與低維拓撲

Stipsicz, Andras, de Bobadilla, Javier Fernández, Marengon, Marco

Singularities and Low Dimensional Topology
  • 出版商: Springer
  • 出版日期: 2024-10-10
  • 售價: $5,590
  • 貴賓價: 9.5 折 $5,311
  • 語言: 英文
  • 頁數: 240
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031566106
  • ISBN-13: 9783031566103

    • 海外代購書籍(需單獨結帳)

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商品描述

The special semester 'Singularities and low dimensional topology' in the Spring of 2023 at the Erdős Center (Budapest) brought together algebraic geometers and topologists to discuss and explore the strong connection between surface singularities and topological properties of three- and four-dimensional manifolds. The semester featured a Winter School (with four lecture series) and several focused weeks. This volume contains the notes of the lecture series of the Winter School and some of the lecture notes from the focused weeks. Topics covered in this collection range from algebraic geometry of complex curves, lattice homology of curve and surface singularities to novel results in smooth four-dimensional topology and grid homology, and to Seiberg-Witten homotopy theory and 'spacification' of knot invariants. Some of these topics are already well-documented in the literature, and the lectures aim to provide a new perspective and fresh connections. Other topics are rather new and have been covered only in research papers. We hope that this volume will be useful not only for advanced graduate students and early-stage researchers, but also for the more experienced geometers and topologists who want to be informed about the latest developments in the field.



商品描述(中文翻譯)

2023年春季在厄爾德什中心（布達佩斯）舉辦的特別學期「奇異性與低維拓撲」聚集了代數幾何學家和拓撲學家，討論並探索表面奇異性與三維和四維流形的拓撲性質之間的密切聯繫。該學期包括一個冬季學校（有四個講座系列）和幾個專注週。本卷包含冬季學校講座系列的筆記以及一些專注週的講座筆記。本合集涵蓋的主題範圍從複曲線的代數幾何、曲線和表面奇異性的格子同調，到平滑四維拓撲和網格同調的新結果，以及Seiberg-Witten同倫論和結不變量的「空間化」。其中一些主題在文獻中已有充分記載，講座旨在提供新的視角和新鮮的聯繫。其他主題則相對較新，僅在研究論文中有所涵蓋。我們希望本卷不僅對高年級研究生和早期研究人員有用，也能對希望了解該領域最新發展的更有經驗的幾何學家和拓撲學家有所幫助。

作者簡介

Javier Fernandez de Bobadilla earned his Ph.D. in 2001, from Nijmegen University. He is currently an Ikerbasque Research Professor at the Basque Center for Applied Mathematics. His interests are at the study of singularities and degenerations from topological, geometric and algebraic methods.

Marco Marengon received his PhD in 2017, and he is currently a senior research fellow at the Rényi Institute in Budapest. His expertise is in low-dimensional topology, including the topology of smooth 4-manifolds and knot invariants such as Heegaard Floer homology and Khovanov homology.

András Némethi received his PhD in 1991, and currently he is a professor at the Rényi Institute and the Eötvös Loránd University in Budapest. His expertise is in singularity theory of complex algebraic (or analytic) varieties and its connections with low dimensional topology. Since 2020 he is member of the Hungarian Academy of Sciences.

András Stipsicz received his PhD in 1994, and currently he is the director (and a professor) of the Rényi Institute in Budapest. His expertise lies in low dimensional topology, especially in the smooth topology of four-manifolds and invariants of three- and four-manifolds, including Seiberg-Witten and Heegaard Floer invariants. Since 2016 he is member of the Hungarian Academy of Sciences.

作者簡介(中文翻譯)

哈維爾·費爾南德斯·德·博巴迪利亞於2001年獲得奈梅亨大學的博士學位。他目前是巴斯克應用數學中心的Ikerbasque研究教授。他的研究興趣集中在從拓撲、幾何和代數方法研究奇點和退化現象。

馬可·馬倫戈於2017年獲得博士學位，目前是布達佩斯雷尼研究所的高級研究員。他的專長是低維拓撲，包括光滑4流形的拓撲以及如Heegaard Floer同調和Khovanov同調等結的不變量。

安德拉斯·內梅提於1991年獲得博士學位，目前是布達佩斯雷尼研究所和厄爾特大學的教授。他的專長是複代數（或解析）多樣體的奇點理論及其與低維拓撲的聯繫。自2020年以來，他是匈牙利科學院的成員。

安德拉斯·斯蒂普西茨於1994年獲得博士學位，目前是布達佩斯雷尼研究所的主任（及教授）。他的專長在於低維拓撲，特別是四流形的光滑拓撲以及三流形和四流形的不變量，包括Seiberg-Witten和Heegaard Floer不變量。自2016年以來，他是匈牙利科學院的成員。

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