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Introductory Lectures on Knot TheoryThis volume consists primarily of survey papers that evolved from the lectures given in the school portion of the meeting and selected papers from the conference. Knot theory is a very special topological subject: the classification of embeddings of a circle or collection of circles into three dimensional space. This is a classical topological problem and a special case of the general placement problem: Understanding the embeddings of a space X in
This volume consists primarily of survey papers that evolved from the lectures given in the school portion of the meeting and selected papers from the conference.Knot theory is a very special topological subject: the classification of embeddings of a circle or collection of circles into three-dimensional space. This is a classical topological problem and a special case of the general placement problem: Understanding the embeddings of a space X in another space Y. There have been exciting new developments in the area of knot theory and 3-manifold topology in the last 25 years. From the Jones, Homflypt and Kauffman polynomials, quantum invariants of 3-manifolds, through, Vassiliev invariants, topological quantum field theories, to relations with gauge theory type invariants in 4-dimensional topology.More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.It is a remarkable fact that knot theory, while very special in its problematic form, involves ideas and techniques that involve and inform much of mathematics and theoretical physics. The subject has significant applications and relations with biology, physics, combinatorics, algebra and the theory of computation. The summer school on which this book is based contained excellent lectures on the many aspects of applications of knot theory. This book gives an in-depth survey of the state of the art of present day knot theory and its applications.Shipping Notes
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★★★★★ 3
Cute
Color: 2-Rose Gold-04
It's cute however it looks rose gold in person. And the chain is very thin. I personally didn't like it and wanted to return it but it was a gift and the person I gave it to loved it and actually loved that it was rose gold. The chain in my opinion was too small.
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Reviewed in the United States on August 29, 2024
★★★★★ 5
Looks exactly as pictured! Simple and elegant!
Color: 2-Rose Gold-11
I love the fact that it looks exactly as pictured, as well as it is simple and elegant!
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Reviewed in the United States on February 4, 2023
★★★★★ 5
Gift for my sil
Color: 2-Rose Gold-05
My sister-in-law loved the necklace. It is her birthstone
Excellent value.
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Reviewed in the United States on February 9, 2025
★★★★★ 5
It is what they say that it is. It is very good quality.
Color: 2-Rose Gold-11
I liked everything about this necklace. It is very good quality. I gave it to my wife for a Christmas present.
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Reviewed in the United States on January 3, 2023
★★★★★ 1
Received wrong color of Gold
Color: 2-Rose Gold-10
It’s pretty, but I ordered Gold and it came in Rose Gold. So I ordered a different necklace for Granddaughter’s Quinceañera next week.
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Reviewed in the United States on October 21, 2023
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