Index A-model, 163, 166, 176, 179, 180, 185 action, 169, 172 correlation function, 168–170, 189, see also Gromov-Witten invariant fermionic symmetry of, see BRST symmetry observable, 169, 176 abelian group, 68 free, 70 homomorphism of, 69, 76 action, 136–137, 143, 146 bosonic string, see string theory, bosonic, action of A-model, see A-model, action supersymmetric, 150, 151 symmetry of, 139, 141 continuous, 139 example of, 141 fermionic, 163 infinitesimal, 140, 143 algebraic curve, 31 isomorphism of, 32 algebraic geometry, 9, 20 angular momentum, 141 antisymmetric product, 61, see also wedge product area form, 160, 171 arithmetic genus, 34 atlas, 50, 58, 60 B-model correlation function, 177, 189 ball, 44, 45 Berezin integral, 149, 153, see also fermionic integration B´ ezout’s theorem, 16, 17, 19, 21, 22, 24, 41, 80–81, 193, 194, see also enumerative geometry, in the plane big quantum cohomology, 191–196 product, 194 associativity of, 194–196 of P1, 194–195 of P2, 195–196 bosonic string action, see string theory, bosonic, action boundary, 54, 72 boundary operator, 71 branch point, 36, 38, 42 BRST cohomology, 166, 168 BRST operator, 166–170, 172 BRST symmetry, 165–170, see also action, symmetry of, fermionic BRST-closed, 168 BRST-exact, 168 CPn, see Pn and complex projective space CP1, see P1 and complex projective line C∞ manifold, see manifold, C∞ Calabi-Yau manifold, 187 definition of, 174 example of, 175 Calabi-Yau threefold, 132, 173–177 definition of, 174 example of, 174 Gromov-Witten invariant of, 176 calculus of variations, 137 canonical bundle, 174, 184 category, 48 example of, 49, 50, 76 201

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