The book is the first systematic research completely devoted to a comprehensive study of virtual knots and classical knots as its integral part. The book is self-contained and contains up-to-date exposition of the key aspects of virtual (and classical) knot theory.Virtual knots were discovered by Louis Kauffman in 1996. When virtual knot theory arose, it became clear that classical knot theory was a small integral part of a larger theory, and studying properties of virtual knots helped one understand better some aspects of classical knot theory and encouraged the study of further problems. Virtual knot theory finds its applications in classical knot theory. Virtual knot theory occupies an intermediate position between the theory of knots in arbitrary three-manifold and classical knot theory.In this book we present the latest achievements in virtual knot theory including Khovanov homology theory and parity theory due to V O Manturov and graph-link theory due to both authors. By means of parity, one can construct functorial mappings from knots to knots, filtrations on the space of knots, refine many invariants and prove minimality of many series of knot diagrams.Graph-links can be treated as “diagramless knot theory”: such “links” have crossings, but they do not have arcs connecting these crossings. It turns out, however, that to graph-links one can extend many methods of classical and virtual knot theories, in particular, the Khovanov homology and the parity theory.
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VIRTUAL KNOTS: THE STATE OF THE ART (Series on Knots and Everything, 51)
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shahidaparveen4452 –
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I like this because he gain my knowledge
sarimrimsa12 –
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“Virtual Knots: The State of the Art is a must-read for anyone delving into modrn knot theory, whether you’re a researcher or an advanced student. This book provides a thorough and accessible overview of virtual knots, covering recent advancments, fundamental concapts, and important open questions in the field. As a part of the esteemed Series on Knots and Everything, it effectively fuses rigorous mathematics with clear explanations that capture the essence of current research trends. With its well-organized structure and acedemic rigor, this volume is perfect for those looking to enhance their understanding of virtual knot theory and stay informed about the latest developments in this niche area of mathmatics.”
mahibilli05 –
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“𝘝𝘪𝘳𝘵𝘶𝘢𝘭 𝘒𝘯𝘰𝘵𝘴: 𝘛𝘩𝘦 𝘚𝘵𝘢𝘵𝘦 𝘰𝘧 𝘵𝘩𝘦 𝘈𝘳𝘵 𝘪𝘴 𝘢𝘯 𝘦𝘯𝘨𝘢𝘨𝘪𝘯𝘨 𝘢𝘯𝘥 𝘮𝘦𝘵𝘪𝘤𝘶𝘭𝘰𝘶𝘴𝘭𝘺 𝘳𝘦𝘴𝘦𝘢𝘳𝘤𝘩𝘦𝘥 𝘣𝘰𝘰𝘬 𝘵𝘩𝘢𝘵 𝘥𝘦𝘭𝘷𝘦𝘴 𝘪𝘯𝘵𝘰 𝘵𝘩𝘦 𝘭𝘢𝘵𝘦𝘴𝘵 𝘢𝘥𝘷𝘢𝘯𝘤𝘦𝘮𝘦𝘯𝘵𝘴 𝘪𝘯 𝘬𝘯𝘰𝘵 𝘵𝘩𝘦𝘰𝘳𝘺, 𝘱𝘳𝘦𝘴𝘦𝘯𝘵𝘪𝘯𝘨 𝘵𝘩𝘦𝘮 𝘸𝘪𝘵𝘩 𝘣𝘰𝘵𝘩 𝘤𝘭𝘢𝘳𝘪𝘵𝘺 𝘢𝘯𝘥 𝘥𝘦𝘱𝘵𝘩. 𝘈𝘴 𝘱𝘢𝘳𝘵 𝘰𝘧 𝘵𝘩𝘦 𝘦𝘴𝘵𝘦𝘦𝘮𝘦𝘥 𝘚𝘦𝘳𝘪𝘦𝘴 𝘰𝘯 𝘒𝘯𝘰𝘵𝘴 𝘢𝘯𝘥 𝘌𝘷𝘦𝘳𝘺𝘵𝘩𝘪𝘯𝘨, 𝘪𝘵 𝘦𝘧𝘧𝘦𝘤𝘵𝘪𝘷𝘦𝘭𝘺 𝘤𝘰𝘯𝘯𝘦𝘤𝘵𝘴 𝘵𝘳𝘢𝘥𝘪𝘵𝘪𝘰𝘯𝘢𝘭 𝘬𝘯𝘰𝘵 𝘵𝘩𝘦𝘰𝘳𝘺 𝘸𝘪𝘵𝘩 𝘵𝘩𝘦 𝘦𝘮𝘦𝘳𝘨𝘪𝘯𝘨 𝘪𝘥𝘦𝘢𝘴 𝘴𝘶𝘳𝘳𝘰𝘶𝘯𝘥𝘪𝘯𝘨 𝘷𝘪𝘳𝘵𝘶𝘢𝘭 𝘬𝘯𝘰𝘵𝘴. 𝘛𝘩𝘦 𝘢𝘶𝘵𝘩𝘰𝘳𝘴 𝘴𝘬𝘪𝘭𝘭𝘧𝘶𝘭𝘭𝘺 𝘢𝘳𝘵𝘪𝘤𝘶𝘭𝘢𝘵𝘦 𝘤𝘰𝘮𝘱𝘭𝘦𝘹 𝘮𝘢𝘵𝘩𝘦𝘮𝘢𝘵𝘪𝘤𝘢𝘭 𝘤𝘰𝘯𝘤𝘦𝘱𝘵𝘴, 𝘮𝘢𝘬𝘪𝘯𝘨 𝘵𝘩𝘦 𝘤𝘰𝘯𝘵𝘦𝘯𝘵 𝘢𝘤𝘤𝘦𝘴𝘴𝘪𝘣𝘭𝘦 𝘢𝘯𝘥 𝘷𝘢𝘭𝘶𝘢𝘣𝘭𝘦 𝘧𝘰𝘳 𝘳𝘦𝘴𝘦𝘢𝘳𝘤𝘩𝘦𝘳𝘴, 𝘨𝘳𝘢𝘥𝘶𝘢𝘵𝘦 𝘴𝘵𝘶𝘥𝘦𝘯𝘵𝘴, 𝘢𝘯𝘥 𝘢𝘯𝘺𝘰𝘯𝘦 𝘸𝘪𝘵𝘩 𝘢 𝘬𝘦𝘦𝘯 𝘪𝘯𝘵𝘦𝘳𝘦𝘴𝘵 𝘪𝘯 𝘵𝘰𝘱𝘰𝘭𝘰𝘨𝘺. 𝘖𝘯𝘪 𝘰𝘧 𝘵𝘩𝘦 𝘣𝘰𝘰𝘬’𝘴 𝘩𝘪𝘨𝘩𝘭𝘪𝘨𝘩𝘵𝘴 𝘪𝘴 𝘪𝘵𝘴 𝘦𝘮𝘱𝘩𝘢𝘴𝘪𝘴 𝘰𝘯 𝘤𝘰𝘯𝘵𝘦𝘮𝘱𝘰𝘳𝘢𝘳𝘺 𝘳𝘦𝘴𝘦𝘢𝘳𝘤𝘩 𝘵𝘳𝘦𝘯𝘥𝘴, 𝘶𝘯𝘳𝘦𝘴𝘰𝘭𝘷𝘦𝘥 𝘲𝘶𝘦𝘴𝘵𝘪𝘰𝘯𝘴, 𝘢𝘯𝘥 𝘨𝘳𝘰𝘶𝘯𝘥𝘣𝘳𝘦𝘢𝘬𝘪𝘯𝘨 𝘵𝘦𝘤𝘩𝘯𝘪𝘲𝘶𝘦𝘴 𝘵𝘩𝘢𝘵 𝘢𝘳𝘦 𝘪𝘯𝘧𝘭𝘶𝘦𝘯𝘤𝘪𝘯𝘨 𝘵𝘩𝘦 𝘧𝘪𝘦𝘭𝘥 𝘵𝘰𝘥𝘢𝘺. 𝘈𝘭𝘵𝘩𝘰𝘶𝘨𝘩 𝘪𝘵 𝘮𝘢𝘺 𝘣𝘦 𝘢 𝘣𝘪𝘵 𝘥𝘢𝘶𝘯𝘵𝘪𝘯𝘨 𝘧𝘰𝘳 𝘣𝘦𝘨𝘪𝘯𝘯𝘦𝘳, 𝘪𝘵 𝘳𝘦𝘮𝘢𝘪𝘯𝘴 𝘢𝘯 𝘪𝘯𝘥𝘪𝘴𝘱𝘦𝘯𝘴𝘢𝘣𝘭𝘦 𝘳𝘦𝘴𝘰𝘶𝘳𝘤𝘦 𝘧𝘰𝘳 𝘵𝘩𝘰𝘴𝘦 𝘢𝘪𝘮𝘪𝘯𝘨 𝘵𝘰 𝘥𝘦𝘦𝘱 𝘵𝘩𝘦𝘪𝘳 𝘶𝘯𝘥𝘦𝘳𝘴𝘵𝘢𝘯𝘥𝘪𝘯𝘨 𝘰𝘧 𝘷𝘪𝘳𝘵𝘶𝘢𝘭 𝘬𝘯𝘰𝘵𝘴 𝘢𝘯𝘥 𝘵𝘩𝘦𝘪𝘳 𝘪𝘯𝘤𝘳𝘦𝘢𝘴𝘪𝘯𝘨 𝘴𝘪𝘨𝘯𝘪𝘧𝘪𝘤𝘢𝘯 𝘪𝘯 𝘮𝘢𝘵𝘩𝘦𝘮𝘢𝘵𝘪𝘤𝘢𝘭 𝘳𝘦𝘴𝘦𝘢𝘳𝘤𝘩.
usamakhan20060 –
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Nice Product
mariam032347.gmc –
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Delve into the forefront of modern knot theory with concise explanations and sophisticated concepts. This engaging book seamlessly integrates mathematics, topology, and innovation, providing readers with a profound grasp of intricate structures. Parfect for inquisitive learners, researchers, and enthusiasts, it offers an insightful and progressive outlook for expanding expertise in this fascinating field.
mariam032347.gmc –
How many times you used this product? 1
Delve into the forefront of modern knot theory with concise explanations and sophisticated concepts. This engaging book seamlessly integrates mathematics, topology, and innovation, providing readers with a profound grasp of intricate structures. Perfect for inquisitive learners, researchers, and enthusiasts, it offers an insightful and progressive outlook for axpanding expertise in this fascinating field.
mariam032347.gmc –
How many times you used this product? 2
Delve into the forefront of modern knot theory with concise explanations and sophisticated concepts. This engaging book seamlessly integrates mathematics, topology, and innovation, providing readers with a profound grasp Ef intricate structures. Perfect for inquisitive learners, researchers, and enthusiasts, it offers an insightful and progressive outlook for expanding expertise in this fascinating field.
haiderrajput712 –
The State of the Art is an excellent resource for anyone with an interest in the fascinating intersection of knots and mathematics. The book presents the principles of virtual knot theory in an accessible manner, enriched with clear examples and illustrations. Whether you’re a student, a researcher, or simply curious about the subject, you’ll find that this book demystifies complex concepts. As part of the renewned Series on Knots and Everything, it highleghts current research and breakthroughs in the field. It’s an ideal starting point for anyone looking to explore this intriguing area of mathematics. If you’re eager to deepen your understanding of knots, this book is a wise and straightforward choice!”
malikhusnaina040 –
VIRTUAL KNOTS: THE STATE OF THE ART (Series on Knots and Everything, 51) it use dby astronaut or moon base research or easy to sell or cheap buy price it is very good to buy again I bought it 4 times and the experience is magical
umairbhatti4640 –
How many times have you used this product ? 2
Good product
miansabmianumair0119 –
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Virtual Knots: The State of the Art is an essential read for anyone fascinated by knot theory and modern mathematics. This comprehensive volume brings together cutting-edge research, expert insights, and clear explanations that make complex ideas accessible and engaging. Whether you’re a student, researcher, or math enthusiast, this book offers a deep dive into virtual knots and their applications, helping you stay ahead in the field. With its authoritative content and uuwell-organized structyure, it serves as both a valuable reference and an inspiring resource. If youf want to expand hyour knowledge and explore the latest advances in knot theory, this book is a must-have addition to your library.
shahidafridikhan926 –
How many times have you used this product ? 3
If you are into math, physics, or just love mind-bending ideas, Virtual Knots: The State of the Art is a really exciting read. The book dives deep into modern knot theory and explains complex concepts in a surprisingly clear way. I liked how it connects virtual knots to real research and current problems, it feels very up to date. Some parts are challanging, but that’s also what makes it rewarding. It’s not just theory, it shows why this topic actually matters today. I did have to reread a few sections twice, but overall it’s inspiring and well written for serious learners.
muhammadsamad960 –
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This graph theory book really help mey in mathematics and physics thanks amazon for this product
hitumaru3107 –
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The VIRTUAL KNOTS: THE STATE OF THE ART is a fascinating book for anyone interested in the mathematics and applications of knots. It explains complex concepts clearly and provides a deep dive into the latest research in the field.
The writing is engaging and the diagrams and examples make the material easier to understand. Whether you’re a student, researcher, or just curious about knots, this book offers valuable insights and knowledge.
Overall, it’s beautifull, informative, and very convenient for learning advanced knot theory. Absolutly recommended for enthusiasts and professionals alike.
jeetbhagat2608 –
How many time have you used this product ? 2
The writing is engaging and the diagrams and examples make the material easier to understand
dishachoudhary2928 –
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Virtual Knots -The State of the Art is an outstanding scholarly work that deliver a comprehensive and authoritative overview of modern developments in virtual knot theory. As part of the respected Series on Knots and Everything, this volume truly lives up to its title, presenting cutting-edge research, rigorous analysis, and deep insights from leading experts in the field.
The book is exceptionally well-structured, guiding readers from foundational concepts to advanced topics with clarity and precision. Complex ideas are explained thoughtfully, supported by detailed illustrations, proofs, and references that make this an invaluable resource for graduate students, researchers, and mathematicians working in topology and knot theory.
What sets this volume apart is its breadth and depth—it not only surveys the current state of research but also highlights open problems and future directions, making it a catalyst for further exploration and innovation. The academic quality, editorial rigor, and contribution to the field are all top-tier.
For anyone serious about knot theory or interested in the evolving landscape of virtual knots, this book is a must-have reference. Scholarly, insightful, and expertly curated highly recommended for academic libraries and specialists alike.
b4s8yu1i27 –
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This engaging book seamlessly integrates mathematics, topology, and innovation, providing readers with a profound grasp of intricate structures.
yadavnikhil1786 –
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Nice book
kunalkarankumar23 –
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Mind bender Dives deep into virtual knot theory a fascinating read if you’re into topology or advanced math. The series on knots is legit and this one’s a solid addition Not for casual readers but great for those who love knot theory
b4s8yu1i27 –
How many time have you used this product ? 2
The writing is engaging and the diagrams and examples make the material easier to understand. Whether you’re a student, researcher, or just curious about knots, this book offers valuable insights and knowledge.
na7108084 –
How many time have you used this product ? 4
A fascinating and well-researchd book for anyone interested in the art and science of knots.
Virtual Knots: The State of the Art presents complex concepts clearly, making it engaging for both beginners and experienced enthusiast.
A great addition to the Series on Knots and Everything.
kumarkartik6626 –
How many time have you used this product ? 2
Good product