Overview
- Provides a glimpse into the interaction of complex singularity theory and low dimensional topology
- Gives a detailed introduction to two instances of 'spacification': Seiberg-Witten homotopy and Khovanov homotopy
- Puts several recent results and constructions into perspective and shows applications of those
Part of the book series: Bolyai Society Mathematical Studies (BSMS, volume 30)
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Keywords
- Heegaard Floer invariants
- Complex curves
- Complex curve singularities
- Isolated surface singularities
- Lattice cohomology
- Knot theory
- Exotic four-manifolds
- Seiberg-Witten invariants
- Monopole Floer Spectra
- Spectra in Khovanov theory
- Spectra in knot Floer theory
- Deformations of curve singularities
- Severi strata
About this book
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.
Editors and Affiliations
About the editors
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.
Bibliographic Information
Book Title: Singularities and Low Dimensional Topology
Editors: Andras Stipsicz, Javier Fernández de Bobadilla, Marco Marengon, András Némethi
Series Title: Bolyai Society Mathematical Studies
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Hardcover ISBN: 978-3-031-56610-3Due: 10 October 2024
Softcover ISBN: 978-3-031-56613-4Due: 10 October 2024
eBook ISBN: 978-3-031-56611-0Due: 10 October 2024
Series ISSN: 1217-4696
Series E-ISSN: 2947-9460
Edition Number: 1