Andras I. Stipsicz – författare
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3 produkter
3 produkter
Häftad, Engelska, 2015
1 639 kr
Skickas inom 11-20 vardagar
Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves.Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology.The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.
Häftad, Engelska, 1999
985 kr
Skickas inom 5-8 vardagar
Since the early 1980s, there has been an explosive growth in 4-manifold theory, particularly due to the influx of interest and ideas from gauge theory and algebraic geometry. This book offers an exposition of the subject from the topological point of view. It bridges the gap to other disciplines and presents classical but important topological techniques that have not previously appeared in the literature.Part I of the text presents the basics of the theory at the second-year graduate level and offers an overview of current research. Part II is devoted to an exposition of Kirby calculus, or handlebody theory on 4-manifolds. It is both elementary and comprehensive. Part III offers in-depth treatments of a broad range of topics from current 4-manifold research. Topics include branched coverings and the geography of complex surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces.The authors present many important applications. The text is supplemented with over 300 illustrations and numerous exercises, with solutions given in the book.
- Nyhet
Häftad, Engelska, 2026
1 332 kr
Skickas inom 11-20 vardagar
This volume is based on lecture series of two Summer Schools in 2024: the Simons Collaboration Summer School "New structures in low-dimensional topology" (Budapest, Hungary) and the Georgia Topology Summer School "Knotted surfaces in four-manifolds" (Athens, Georgia, USA). These notes provide a glimpse to several novel methods and results in low dimensional topology. Indeed, the lectures on "Instanton Floer homology and applications" (by Mrowka and Baldwin) give a detailed account on instanton invariants, apply it in the sutured setting, and provide results regarding the minimal genus problem. Novel invariants are discussed in the lectures of Gukov and Park and provide a close connection to theoretical physics. The lectures of Lobb and Greene on the square peg problem give an up-to-date account regarding the solution of this simple-looking, more than 100 years old problem on the plane. The lectures of Maggie Miller describe knotted surfaces in the 4-dimensional sphere, while the lectures of Mark Hughes provide a diagrammatic approach to the same problem. Arunima Ray's lectures also deal with surfaces, but in this case, the embedding is not necessarily smooth, only 'locally flat'. Kyle Hayden’s lectures connect link homologies to the study of surfaces in four-dimensional spaces. Finally, the lectures of Stipsicz recall the construction of invariants for four-dimensional manifolds and examine the genus function of a four-manifold using these tools.