Singularities and Low Dimensional Topology

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: $5,530
  • 貴賓價: 9.5 折 $5,254
  • 語言: 英文
  • 頁數: 240
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031566106
  • ISBN-13: 9783031566103

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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，位於布達佩斯的Erdős Center舉辦了一個名為「奇異點與低維拓撲」的特別學期，聚集了代數幾何學家和拓撲學家，討論和探索了曲面奇異點與三維和四維流形的拓撲性質之間的強烈聯繫。該學期包括一個冬季學校（有四個講座系列）和幾個專題週。本書收錄了冬季學校的講座系列筆記和部分專題週的講座筆記。本書涵蓋的主題範圍從複雜曲線的代數幾何學、曲線和曲面奇異點的格子同調性到平滑四維拓撲和網格同調性的新結果，以及Seiberg-Witten同伦理論和結網不變量的「空間化」。其中一些主題已經在文獻中有詳細記錄，講座旨在提供新的觀點和新的聯繫。其他主題則相對較新，只在研究論文中有涉及。我們希望本書不僅對高級研究生和初級研究人員有用，也對更有經驗的幾何學家和拓撲學家有用，他們希望了解該領域的最新發展。

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)

Javier Fernandez de Bobadilla於2001年在Nijmegen大學獲得博士學位，目前是巴斯克應用數學中心的Ikerbasque研究教授。他的研究興趣涉及從拓撲、幾何和代數方法研究奇異點和退化現象。

Marco Marengon於2017年獲得博士學位，目前是布達佩斯Rényi研究所的高級研究員。他的專業領域是低維拓撲學，包括光滑四維流形的拓撲和結繩不變量，如Heegaard Floer同調和Khovanov同調。

András Némethi於1991年獲得博士學位，目前是布達佩斯Rényi研究所和Eötvös Loránd大學的教授。他的專業領域是複雜代數（或解析）變量的奇異點理論及其與低維拓撲的聯繫。自2020年起，他成為匈牙利科學院的成員。

András Stipsicz於1994年獲得博士學位，目前是布達佩斯Rényi研究所的所長（兼教授）。他的專業領域是低維拓撲學，特別是四維流形的光滑拓撲和三維、四維流形的不變量，包括Seiberg-Witten和Heegaard Floer不變量。自2016年起，他成為匈牙利科學院的成員。

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