When Topology Meets Chemistry: A Topological Look at Molecular Chirality

by Erica Flapan

• ISBN13: 9780521664820
• ISBN10: 0521664829
• Format: Paperback
• Copyright: 2000-07-31
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Preface	xi
Stereochemical Topology	1	(31)
Examples of Topologically Complex Molecules	2	(5)
Stereoisomers	7	(6)
Chirality	13	(2)
Chirality of Mobius Ladders	15	(4)
Intrinsic Chirality	19	(1)
Euclidean Rubber Gloves	19	(2)
Topological Rubber Gloves	21	(4)
Nonrigid Symmetries	25	(4)
Exercises	29	(3)
Detecting Chirality	32	(37)
Defining Chirality	33	(6)
Knot and Link Types	39	(2)
Link Polynomials	41	(7)
Chirality of Embedded Graphs	48	(4)
Chirality of Molecular Knots and Links	52	(5)
Alternating Links	57	(6)
Tait's Conjecture	63	(3)
Exercises	66	(3)
Mobius Ladders and Related Molecular Graphs	69	(41)
Chirality of Mobius Ladders	69	(21)
Intrinsic Chirality	90	(8)
Triple-Layered Naphthalenophane	98	(7)
Multiply Twisted Closed Ladders	105	(2)
Exercises	107	(3)
Different Types of Chirality and Achirality	110	(26)
Topological Rubber Gloves in R3	114	(4)
Molecular Topological Rubber Gloves	118	(6)
Intrinsic Topological Rubber Gloves	124	(1)
Hierarchies of Achirality	125	(3)
Molecular Cell Complexes	128	(6)
Exercises	134	(2)
Intrinsic Topological Properties of Graphs	136	(25)
Results of Conway and Gordon	137	(3)
Minor Minimal Intrinsically Linked Graphs	140	(4)
ΔY Moves and Intrinsic Knottedness	144	(4)
Intrinsic Chirality of Complete Graphs	148	(7)
Topological Stereoisomers	155	(5)
Exercises	160	(1)
Symmetries of Embedded Graphs	161	(37)
Nonrigid Symmetries	162	(1)
Rigid Symmetries of Three-Connected Graphs	163	(9)
Topological Chirality of Labeled Graphs	172	(4)
Using Automorphisms to Show Intrinsic Chirality	176	(2)
Symmetries of Complete Graphs	178	(14)
Hierarchies of Automorphisms	192	(3)
Exercises	195	(3)
Topology of DNA	198	(35)
Supercoiling	201	(6)
Toroidal Winding of DNA	207	(3)
The Action of Enzymes on DNA	210	(4)
Conway's Theory of Tangles	214	(5)
Results of Ernst and Sumners	219	(12)
Exercises	231	(2)
References	233	(6)
Index	239