Index (2, m)-torus knot or link, 51 K5, 37 K3,3, 37 T (2, m), 51 W r, 52 α0, 55 λ Int, 65 σ, specific linking difference, 53 T , 70 2-fold branched covers, 32 4-plat, 69 4-plats, 59 accessory proteins, 64 Adenine, 48 agarose gel electrophoresis, 61 Alexander theorem, 85 alternating knots, 7, 11 ambient isotopy, 83 antibiotics, 57 antijunction, 131 anyons, 118 Artin Braid Group, 84 atomic force microscopy, 133 automorphism group of Γ, 41 automorphism of a graph, 36 average crossing number (ACN), 9, 159–162, 171–178 B-DNA, 122 B-Z transition, 135 base-stacking, 124 Berge, John, 60 Bleiler, S., 69 Bohr, Niels, 94 Borromean rings, 84, 122 bounds for ropelength, 169 bounds on tangling (ACN), 176, 177 bracket polynomial, 14, 85, 87 braid, 84 braid index, 7, 18 branched junctions, 123 bridge index, 5 bridge number, 170 Buck, D., 65, 73 Buck, G., 58 C˘ alug˘ areanu, G., 50 catenanes, 50, 122 chemical symmetry group, 43 chemically achiral, 25 chemically chiral, 25 Chern-Simons action, 105 compaction, 166, 171, 177 complete bipartite graph on two sets of three vertices, 37 complete graph on five vertices, 37 composite knot, 3 composition, 3, 5, 6, 12, 15 conformation, 2 connection, 107 connectivity, 124 constant curvature, 168 Conway, J.H., 68 Cozzarelli, N.R., 68 Cre, 65 Crick, Francis, 48 Crisona, N.J., 72 crossing index, 2, 17, 18 crossing number, 170, 174, 175 crossing sphere, 9, 16 crossover sites, 63 crossovers, 126 cube, 128 curvature, 51, 164, 166, 168, 170 Cytosine, 48 Darcy, Isabel, K., 60 DeBroglie, 94, 95, 96 Einstein, 96 Dennis, M.R., 53 Deoxyribonucleic Acid, 48 design, 124 distance between two vertices, 37 distributive recombination, 64 DNA, 48, 121, 157, 166, 172 gyrase, 57 origami, 139 183

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