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Kronecker
first limit formula, 490 |
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Künneth
formula, 199–200 |
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Laplacian,
254 |
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elliptic
complex, 410 |
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Hermitian
manifold, 294 |
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Kähler
manifold, 295 |
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Riemann
surface, 465–6 |
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Left-invariant
vector field, 170, 329 |
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Left-translation,
170 |
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Letter,
102 |
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Levi-Civita
connection, 209, 214, 221–3, 240, 247–9 |
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classical
differential geometry, 223 |
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Levi-Civita
symbol, 160 |
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Lie
algebra, 172–3, 329–30 |
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Lie
bracket, 154 |
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Lie
derivative, 153–7, 163–4 |
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Lie
group, 167–70, 221, 305, 324–5, 329–30 |
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Light
cone frame, 206 |
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Lightlike,
205, 236 |
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Line
bundle, 314, 387 |
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holomorphic,
463 |
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Linear
function, 43 |
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Linear
map, 43 |
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Linear
space, 43 |
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Linearly
dependent, 43 |
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Linearly
independent, 43, 64 |
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Abelian
group, 64 |
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vector
space, 43 |
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Liquid
crystal, 24–5 |
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defects,
121–5 |
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nematic,
25 |
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Little
group, 181 |
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Local
connection form, 332–6 |
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Local
frame, 246–7 |
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Local
section, 305, 307 |
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Local
trivialisation, 305 |
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London
limit, 22 |
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Loop,
90, 114 |
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Lorentz
condition, 186, 255 |
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Lorentz
manifold, 206 |
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Lorentz
metric, 205 |
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Magnetic
monopole, 14–17 |
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Berry's
phase, 370 |
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Dirac,
14 |
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Dirac
quantisation condition, 16 |
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principal
bundle, 320, 335, 355–6, 386 |
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Wu–Yang,
15, 371 |
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Manifold,
131–40 |
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differentiable,
133 |
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with
a boundary, 134, 429 |
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Map,
35 |
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linear,
43 |
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Mapping
class group (MCG), 470 |
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Matrix
group, 168 |
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Maurer–Cartan
form, 176 |
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Maurer–Cartan's
structure equation, 176 |
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Maximally
symmetric space, 241 |
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Maxwell
action, 355 |
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Maxwell's
equation, 10, 14, 255, 355 |
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Mellin
transformation, 428, 430 |
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Mermin–Ho
vortex, 127 |
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Metric,
49 |
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Metric
compatible, 214, 247, 285 |
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Metric
connection, 214, 351 |
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Metric
space, 49 |
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Metric
tensor, 27 |
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Milne
universe, 239 |
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Minkowski
metric, 205 |
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Möbius
strip, 39, 165, 308, 328 |
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fundamental
group, 112 |
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homology
group, 79 |
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Moduli
space, |
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gauge
theory, 446 |
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Polyakov
string, 470, 487 |
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Modular
group (MG), 470 |
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Modular
parameter, 270 |
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Modular
transformation, 270 |
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Nambu
action, 32, 262 |
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Naturality,
379, 382, 384, 387 |
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Neighbourhood,
50 |
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open,
50 |
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Nijenhuis
tensor field, 298–300 |
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Non-coordinate
basis, 145, 243–5 |
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Non-orientable,
39 |
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Normal
bundle, 314 |
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Normal
coordinate system, 228 |
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Normal
subgroup, 42, 169 |
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