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When Topology Meets Chemistry : A Topological Look at Molecular Chirality - Erica Flapan

When Topology Meets Chemistry

A Topological Look at Molecular Chirality

Paperback Published: 1st December 2000
ISBN: 9780521664820
Number Of Pages: 256

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The applications of topological techniques for understanding molecular structures have become increasingly important over the past thirty years. In this topology text, the reader will learn about knot theory, 3-dimensional manifolds, and the topology of embedded graphs, while learning the role these play in understanding molecular structures. Most of the results that are described in the text are motivated by questions asked by chemists or molecular biologists, though the results themselves often go beyond answering the original question asked. There is no specific mathematical or chemical prerequisite; all the relevant background is provided. The text is enhanced by nearly 200 illustrations and more than 100 exercises. Reading this fascinating book, undergraduate mathematics students can escape the world of pure abstract theory and enter that of real molecules, while chemists and biologists will find simple, clear but rigorous definitions of mathematical concepts they handle intuitively in their work.

Industry Reviews

'If you are a chemist ... looking for applications of low dimensional topology in the natural sciences, this is a book you should own ... serves as an excellent introduction to the field for a topologist looking for interesting applications of topology in science. The book is well produced with many useful diagrams and with exercises that range from easy to intriguing. This book is definitely on my 'buy list'.' Stuart Whittington, SIAM Review

Prefacep. xi
Stereochemical Topologyp. 1
Examples of Topologically Complex Moleculesp. 2
Stereoisomersp. 7
Chiralityp. 13
Chirality of Mobius Laddersp. 15
Intrinsic Chiralityp. 19
Euclidean Rubber Glovesp. 19
Topological Rubber Glovesp. 21
Nonrigid Symmetriesp. 25
Exercisesp. 29
Detecting Chiralityp. 32
Defining Chiralityp. 33
Knot and Link Typesp. 39
Link Polynomialsp. 41
Chirality of Embedded Graphsp. 48
Chirality of Molecular Knots and Linksp. 52
Alternating Linksp. 57
Tait's Conjecturep. 63
Exercisesp. 66
Mobius Ladders and Related Molecular Graphsp. 69
Chirality of Mobius Laddersp. 69
Intrinsic Chiralityp. 90
Triple-Layered Naphthalenophanep. 98
Multiply Twisted Closed Laddersp. 105
Exercisesp. 107
Different Types of Chirality and Achiralityp. 110
Topological Rubber Gloves in R[superscript 3]p. 114
Molecular Topological Rubber Glovesp. 118
Intrinsic Topological Rubber Glovesp. 124
Hierarchies of Achiralityp. 125
Molecular Cell Complexesp. 128
Exercisesp. 134
Intrinsic Topological Properties of Graphsp. 136
Results of Conway and Gordonp. 137
Minor Minimal Intrinsically Linked Graphsp. 140
[Delta] Y Moves and Intrinsic Knottednessp. 144
Intrinsic Chirality of Complete Graphsp. 148
Topological Stereoisomersp. 155
Exercisesp. 160
Symmetries of Embedded Graphsp. 161
Nonrigid Symmetriesp. 162
Rigid Symmetries of Three-Connected Graphsp. 163
Topological Chirality of Labeled Graphsp. 172
Using Automorphisms to Show Intrinsic Chiralityp. 176
Symmetries of Complete Graphsp. 178
Hierarchies of Automorphismsp. 192
Exercisesp. 195
Topology of DNAp. 198
Supercoilingp. 201
Toroidal Winding of DNAp. 207
The Action of Enzymes on DNAp. 210
Conway's Theory of Tanglesp. 214
Results of Ernst and Sumnersp. 219
Exercisesp. 231
Referencesp. 233
Indexp. 239
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521664820
ISBN-10: 0521664829
Series: Outlooks
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 256
Published: 1st December 2000
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 1.91
Weight (kg): 0.34

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