When Topology Meets Chemistry A Topological Look at Molecular Chirality

ISBN-10: 0521664829
ISBN-13: 9780521664820
Edition: 2000
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Description: 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  More...

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Book details

Copyright year: 2000
Publisher: Cambridge University Press
Publication date: 7/31/2000
Binding: Paperback
Pages: 256
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 0.968
Language: English

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.

Persi Diaconis is professor of mathematics and statistics at Stanford University and a professional magician. Ron Graham is professor of mathematics and computer science at the University of California, San Diego, and a professional juggler.

Preface
Stereochemical Topology
Examples of Topologically Complex Molecules
Stereoisomers
Chirality
Chirality of Mobius Ladders
Intrinsic Chirality
Euclidean Rubber Gloves
Topological Rubber Gloves
Nonrigid Symmetries
Exercises
Detecting Chirality
Defining Chirality
Knot and Link Types
Link Polynomials
Chirality of Embedded Graphs
Chirality of Molecular Knots and Links
Alternating Links
Tait's Conjecture
Exercises
Mobius Ladders and Related Molecular Graphs
Chirality of Mobius Ladders
Intrinsic Chirality
Triple-Layered Naphthalenophane
Multiply Twisted Closed Ladders
Exercises
Different Types of Chirality and Achirality
Topological Rubber Gloves in R[superscript 3]
Molecular Topological Rubber Gloves
Intrinsic Topological Rubber Gloves
Hierarchies of Achirality
Molecular Cell Complexes
Exercises
Intrinsic Topological Properties of Graphs
Results of Conway and Gordon
Minor Minimal Intrinsically Linked Graphs
[Delta] Y Moves and Intrinsic Knottedness
Intrinsic Chirality of Complete Graphs
Topological Stereoisomers
Exercises
Symmetries of Embedded Graphs
Nonrigid Symmetries
Rigid Symmetries of Three-Connected Graphs
Topological Chirality of Labeled Graphs
Using Automorphisms to Show Intrinsic Chirality
Symmetries of Complete Graphs
Hierarchies of Automorphisms
Exercises
Topology of DNA
Supercoiling
Toroidal Winding of DNA
The Action of Enzymes on DNA
Conway's Theory of Tangles
Results of Ernst and Sumners
Exercises
References
Index

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