When Topology Meets Chemistry: A Topological Look at Molecular ChiralityCambridge University Press, 2000 M07 31 - 241 pages 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. |
Contents
I | ix |
II | x |
III | 1 |
IV | 7 |
V | 9 |
VI | 13 |
VIII | 15 |
IX | 19 |
XXX | 120 |
XXXI | 126 |
XXXII | 128 |
XXXIII | 129 |
XXXIV | 132 |
XXXV | 136 |
XXXVI | 140 |
XXXVII | 147 |
X | 23 |
XI | 26 |
XII | 27 |
XIII | 33 |
XIV | 35 |
XV | 40 |
XVI | 44 |
XVII | 49 |
XVIII | 55 |
XIX | 58 |
XX | 61 |
XXI | 82 |
XXII | 90 |
XXIII | 97 |
XXIV | 99 |
XXV | 102 |
XXVI | 106 |
XXVII | 110 |
XXVIII | 116 |
XXIX | 117 |
XXXVIII | 152 |
XXXIX | 153 |
XL | 154 |
XLI | 155 |
XLII | 164 |
XLIII | 168 |
XLIV | 170 |
XLV | 184 |
XLVI | 187 |
XLVII | 190 |
XLVIII | 193 |
XLIX | 199 |
L | 202 |
LI | 206 |
LII | 211 |
LIII | 223 |
LIV | 225 |
LV | 231 |
Other editions - View all
When Topology Meets Chemistry: A Topological Look at Molecular Chirality Erica Flapan Limited preview - 2000 |
When Topology Meets Chemistry: A Topological Look at Molecular Chirality Erica Flapan Limited preview - 2000 |
When Topology Meets Chemistry: A Topological Look at Molecular Chirality Erica Flapan No preview available - 2000 |
Common terms and phrases
ambient isotopic automorphism bond graph boundary cell complex chemically circle complete graph component contains define definition deformed denote disjoint DNA molecule edges embedded graph embedded in R3 embedding of G enzyme example figure eight knot finite-order homeomorphism Flapan gluing graph G half-twists helix axis Hence hexagons homeomorphism of R3 Hopf link illustrated in Figure induced intrinsically chiral intrinsically knotted invariant K₁ knot or link knots and links labeled graph Lemma link is topologically linking number mirror image Möbius ladder Möbius strip molecular graph obtain orbit of order orientation preserving orientation reversing orientation-preserving homeomorphism orientation-reversing homeomorphism oriented link P-polynomial pair planar plane polynomial proof prove rational tangle reduced alternating projection rotation Seifert surface side simple closed curve solid torus strands supercoiled Suppose surface symmetry presentation three-dimensional three-manifold topological rubber glove topological stereoisomers topologically chiral trefoil knot twist twofold branched cover unknot unoriented link writhe