336 Index edge density, 314 elementary set, 322 equivariant map, 298 escape norm, 201 existence and uniqueness of Haar measure, 78 exponential coordinates, 41 exponential map, 69 extension problem, 277 faithful action, 127 finite trapping, 114 formal commutator word, 243 formal predicate, 157 Fourier analysis on compact abelian groups, 94 Fourier inversion formula, 303 Freiman’s theorem, 17, 164 Fubini-Tonelli theorem, 314 gauge transformation, 281 general linear group, 9 generalised arithmetic progression, 16, 164 Gleason lemma, 202 Gleason metric, 55 Gleason-Yamabe theorem for abelian groups, 96 Gleason-Yamabe theorem for compact groups, 92 good model, 185, 213 Gromov’s theorem, 21, 224 Gromov-Hausdorff distance, 171 group cohomology, 281 group germ, 267 group of polynomial growth, 21 Haar measure, 77, 87 Hadamard lemma, 46 half-open topology, 62 Hall-Witt identity, 240 hard analysis, 139 Hausdorff distance, 116, 170 height, 308 Heisenberg group, 9 Helfgott-Lindenstrauss conjecture, 216 Hilbert’s fifth problem, 10, 133 Hilbert-Smith conjecture, 289 homogeneous space, 86 homomorphism, 29 Hrushovski Lie model theorem, 213 Hrushovski’s Lie model theorem, 192, 195 Hrushovski’s structure theorem, 194 hyperreal, 149 indicator function, xiii infinitesimal, 159 infinitesimal part, 159 inner regularity, 77 internal function, 152 internal set, 149 invariance of dimension, 126 invariance of domain, 126, 132 inverse limit, 93 irreducible representation, 298 isotypic component, 300 Jacobi identity, 249 Jordan’s theorem, 6, 233 Jordan-Schur theorem, 233 Keisler-Fubini theorem, 319 lamplighter group, 191 left-invariant vector field, 34 Leibniz rule, 33 Levi’s theorem, 258 Lie algebra, 33 Lie algebra of a Lie group, 34 Lie bracket, 33 Lie group, 8 Lie groups are analytic, 49 Lie’s first theorem, 40 Lie’s second theorem, 50 Lie’s third theorem, 35, 50, 270 lifting lemma, 215 local finiteness, 77 local Gleason metric, 121 local Gleason-Yamabe theorem, 121 local group, 26 local Haar measure, 86 local homomorphism, 29 local Lie group, 27 Local Lie implies Lie, 43 local section, 283 local topological group, 26 Loeb measure, 317 Los’s theorem, 154 lower central series, 241 Margulis-type lemma, 229 matrix exponential, 4 measure space, 313
Previous Page Next Page