When Topology Meets Chemistry: A Topological Look at Molecular Chirality
In this superb topology text, the readers not only learn about knot theory, 3-dimensional manifolds, and the topology of embedded graphs, but also their role in understanding molecular structures. Most results described in the text are motivated by the questions of chemists or molecular biologists, though they often go beyond answering the original question asked. No specific mathematical or chemical prerequisites are required. The text is enhanced by nearly 200 illustrations and 100 exercises. With this fascinating book, undergraduate mathematics students escape the world of pure abstract theory and enter that of real molecules, while chemists and biologists find simple and clear but rigorous definitions of mathematical concepts they handle intuitively in their work.
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achiral in R3 ambient isotopic Arf invariant 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 gluing graph G half-twists helix axis Hence hexagons homeomorphism of R3 Hopf link illustrated in Figure induced intrinsically chiral intrinsically knotted invariant knot or link knots and links labeled graph Lemma link is topologically linking number mirror image molecular graph negative achiral obtain orbit of order orientation preserving orientation reversing orientation-preserving homeomorphism orientation-reversing homeomorphism oriented link P-polynomial pair planar plane polynomial 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