Page 501

		Hodge's theorem, 257

		Hermitian manifold, 294

		Holomorphic, 265

		form, 280, 295

		function, 273

		map, 273

		tangent bundle, 352

		vector, 277

		vector bundle, 352

		vector field, 277

		Holonomy group,

		Berry's phase, 368

		Kähler manifold, 291–2

		principal bundle, 339–40, 343

		restricted, 340

		Riemannian geometry, 232–4

		Homeomorphism, 53–9

		Homogeneous coordinate, 137, 271

		Homogeneous space, 181

		Homologous, 75

		Homology class, 75

		Homology group, 74–84

		general property, 84–7

		singular, 189

		Homomorphism, 37

		Abelian group, 62

		fundamental theorem, 63

		Homotopic, 91, 96, 114, 201, 312, 328

		Homotopy, 91–3, 96, 114

		class, 93, 114

		equivalence, 96

		inverse, 96

		Homotopy group, 93, 113–18

		Homotopy operator, 399

		Homotopy type, 55–6, 59, 96

		Hopf invariant, 328

		Hopf map, 322–4

		Horizontal lift, 336–9, 346

		Horizontal subspace, 330–2

		I

		Identity map, 37

		Image, 35, 43

		Immersion, 149

		Inclusion map, 37

		Index, of elliptic complex, 410

		Index, of metric, 205

		Index theorem, 47

		Atiyah–Patodi–Singer, 430–3, 459

		Atiyah–Singer, 412–13, 440

		Callias–Bott–Seely, 433

		vector space, 47

		Induced metric, 206

		Induced vector field, 184

		Inhomogeneous coordinate, 137, 271

		Injective, 36

		Inner product, 45

		differential forms, 253

		one-form and vector, 146

		Riemann surface, 465

		vector space, 45, 46

		Instanton, 17–19

		principal bundle, 320–2, 360–4, 386, 424

		Instanton number, 321, 446

		Integrable, almost complex structure, 298

		Integral curve, 150

		Interior, 50

		Interior product, 162–4

		Invariant, 374

		Invariant polynomial, 375

		Invariant volume element, 250

		Inverse image, 35

		Inverse map, 37

		Isometry, 234, 239

		Isomorphism, 37

		Abelian group, 62

		vector space, 43

		Isothermal coordinate, 239, 263, 461

		Isotropy group, 181

		J

		J-homomorphism, 120

		K

		Kähler form, 282–3

		Kähler manifold, 287–90, 295–6

		Kähler metric, 287

		Kähler potential, 288

		Kernel, 43

		linear map, 43

		Killing equation, 240

		Killing vector field, 239–42

		Klein bottle, 40

		fundamental group, 110

		homology group, 83