Topology for PhysicistsSpringer Science & Business Media, 16 juil. 1996 - 296 pages In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. Topology has profound relevance to quantum field theory-for example, topological nontrivial solutions of the classical equa tions of motion (solitons and instantons) allow the physicist to leave the frame work of perturbation theory. The significance of topology has increased even further with the development of string theory, which uses very sharp topologi cal methods-both in the study of strings, and in the pursuit of the transition to four-dimensional field theories by means of spontaneous compactification. Im portant applications of topology also occur in other areas of physics: the study of defects in condensed media, of singularities in the excitation spectrum of crystals, of the quantum Hall effect, and so on. Nowadays, a working knowledge of the basic concepts of topology is essential to quantum field theorists; there is no doubt that tomorrow this will also be true for specialists in many other areas of theoretical physics. The amount of topological information used in the physics literature is very large. Most common is homotopy theory. But other subjects also play an important role: homology theory, fibration theory (and characteristic classes in particular), and also branches of mathematics that are not directly a part of topology, but which use topological methods in an essential way: for example, the theory of indices of elliptic operators and the theory of complex manifolds. |
Table des matières
I | 1 |
II | 4 |
III | 6 |
IV | 9 |
V | 11 |
VI | 13 |
VII | 16 |
VIII | 19 |
XLI | 149 |
XLII | 159 |
XLIV | 161 |
XLV | 163 |
XLVI | 164 |
XLVII | 167 |
XLVIII | 170 |
XLIX | 173 |
IX | 21 |
X | 23 |
XI | 30 |
XII | 33 |
XIII | 37 |
XIV | 41 |
XV | 42 |
XVI | 45 |
XVII | 49 |
XVIII | 53 |
XIX | 55 |
XX | 56 |
XXI | 59 |
XXII | 64 |
XXIII | 67 |
XXIV | 70 |
XXV | 72 |
XXVI | 73 |
XXVII | 74 |
XXVIII | 77 |
XXIX | 87 |
XXX | 94 |
XXXI | 98 |
XXXII | 101 |
XXXIII | 103 |
XXXIV | 117 |
XXXV | 125 |
XXXVI | 127 |
XXXVII | 130 |
XXXVIII | 139 |
XXXIX | 143 |
XL | 145 |
L | 175 |
LI | 177 |
LII | 181 |
LIII | 185 |
LIV | 187 |
LV | 191 |
LVI | 193 |
LVII | 196 |
LVIII | 199 |
LIX | 209 |
LX | 211 |
LXI | 212 |
LXII | 217 |
LXIII | 218 |
LXIV | 223 |
LXV | 226 |
LXVI | 228 |
LXVII | 233 |
LXIX | 236 |
LXX | 243 |
LXXI | 247 |
LXXII | 251 |
LXXIII | 254 |
LXXIV | 263 |
LXXV | 266 |
LXXVI | 268 |
LXXVII | 270 |
LXXVIII | 274 |
LXXIX | 287 |
289 | |
295 | |
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Expressions et termes fréquents
action of G algebra g antisymmetric Betti number boundary called cell decomposition characteristic classes charts cochain coefficients cohomology class coincides compute consider construction coordinate system covering curve cycle defined definition denote dimension direct sum dx¹ element equation example fiber fibration finite follows function ƒ and g gauge field given GL(n gluing H(X mod homeomorphic homology groups homotopy class homotopy lifting property identity integral invariant isomorphic jacobian k-cycle k-dimensional k-form Lie algebra Lie group G linear loop map f map Sk matrix metric modulo neighborhood nonzero null-homotopic obtained one-to-one correspondence open set open subset orbit oriented principal fibration quotient regarded Riemannian Riemannian metric satisfies scalar product Section sequence simply connected singular smooth manifold smooth map SO(n sphere spheroid SU(n subgroup subspace takes tangent vector tensor theorem topological space transformations trivial U₁ vector field vector space w₁ zero