Knots, links and their invariants: an elementary course in contemporary knot theory

By:

Sossinsky, A. B

Series: Student Mathematical Library, Volume 101Publication details: Providence, Rhode Island: American Mathematical Society, 2023.Description: xvii, 128p.: ill.; pbk.: 22cmISBN:

9781470471514

Subject(s):

DDC classification:

514.2242 SOS

Summary: This book is an elementary introduction to knot theory. Unlike many other books on knot theory, this book has practically no prerequisites; it requires only basic plane and spatial Euclidean geometry but no knowledge of topology or group theory. It contains the first elementary proof of the existence of the Alexander polynomial of a knot or a link based on the Conway axioms, particularly the Conway skein relation. The book also contains an elementary exposition of the Jones polynomial, HOMFLY polynomial and Vassiliev knot invariants constructed using the Kontsevich integral. Additionally, there is a lecture introducing the braid group and shows its connection with knots and links. Other important features of the book are the large number of original illustrations, numerous exercises and the absence of any references in the first eleven lectures. The last two lectures differ from the first eleven: they comprise a sketch of non-elementary topics and a brief history of the subject, including many references. https://bookstore.ams.org/view?ProductCode=STML/101

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar	General	514.2242 SOS (Browse shelf(Opens below))	1	Available		034079

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Previous	514.224 KAS Categories and sheaves	514.224 KAS Sheaves on manifolds	514.224 KAU Knots and physics	514.2242 SOS Knots, links and their invariants: an elementary course in contemporary knot theory	514.23 GIL Central Simple algebras and Galois cohomology	514.23 HIG Analytic k homology	514.23 MAD From calculus to cohomology: de Rham cohomology and characteristic classes	Next

Includes index.

This book is an elementary introduction to knot theory. Unlike many other books on knot theory, this book has practically no prerequisites; it requires only basic plane and spatial Euclidean geometry but no knowledge of topology or group theory. It contains the first elementary proof of the existence of the Alexander polynomial of a knot or a link based on the Conway axioms, particularly the Conway skein relation. The book also contains an elementary exposition of the Jones polynomial, HOMFLY polynomial and Vassiliev knot invariants constructed using the Kontsevich integral. Additionally, there is a lecture introducing the braid group and shows its connection with knots and links.

Other important features of the book are the large number of original illustrations, numerous exercises and the absence of any references in the first eleven lectures. The last two lectures differ from the first eleven: they comprise a sketch of non-elementary topics and a brief history of the subject, including many references.

https://bookstore.ams.org/view?ProductCode=STML/101

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