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Название: Foliations I
Авторы: Candel A., Conlon L.
Аннотация:
This is the first of two volumes on the qualitative theory of foliations. This volume is divided into three parts. It is extensively illustrated throughout and provides a large number of examples. Part 1 is intended as a "primer" in foliation theory. A working knowledge of manifold theory and topology is a prerequisite. Fundamental definitions and theorems are explained to prepare the reader for further exploration of the topic. This section places considerable emphasis on the construction of examples, which are accompanied by many illustrations.
Part 2 considers foliations of codimension one. Using very hands-on geometric methods, the path leads to a complete structure theory (the theory of levels), which was established by Conlon along with Cantwell, Hector, Duminy, Nishimori, Tsuchiya, et al. Presented here is the first and only full treatment of the theory of levels in a textbook.
Part 3 is devoted to foliations of higher codimension, including abstract laminations (foliated spaces). The treatment emphasizes the methods of ergodic theory: holonomy-invariant measures and entropy. Featured are Sullivan's theory of foliation cycles, Plante's theory of growth of leaves, and the Ghys, Langevin, Walczak theory of geometric entropy.
This comprehensive volume has something to offer a broad spectrum of readers: from beginners to advanced students to professional researchers. Packed with a wealth of illustrations and copious examples at varying degrees of difficulty, this highly-accessible text offers the first full treatment in the literature of the theory of levels for foliated manifolds of codimension one. It would make an elegant supplementary text for a topics course at the advanced graduate level. Foliations II is Volume 60 in the AMS in the Graduate Studies in Mathematics series.
Foliation(s), transversely affine42373 Foliation(s), transversely homogeneous34 Foliation(s), transversely Lie34 Foliation(s), transversely orientable28 Foliation(s), transversely Riemannian33 Form on a foliated space301 Form, closed, defining foliation24 Form, closed, group of periods of42 Form, closed, periods of2441 Form, defining foliation24 Form, distributional231 Form, transverse to a foliation240265 Frobenius theorem34—43 Frobenius Theorem, statement of37 Frobenius theorem, vector field version36 Fundamental domain72 G-orbit18282285 G-orbit, global286 G-orbit, local286 Gabai, D.197 Gauss — Bonnet theorem148331 General position151—164 General position, definition of152 Geodesic spray88 Geodesic spray, leafwise89 Germ(s) of a foliation63 Germ(s) of a local homeomorphism60 Germ(s), isomorphic (of foliations)63 Germinal holonomy59—67 Ghys, E.194229345358360374 Gluck, H.266 Glue18 Gluing, tangential90 Gluing, transverse81 Godbillon — Vey class3899192 Godbillon — Vey class of Hirsch foliation373 Godbillon — Vey class, generalized40 Godbillon — Vey class, invariance, under concordance101 Godbillon — Vey class, invariance, under integrable homotopy101 Godbillon — Vey class, invariance, under isotopy101 Godbillon — Vey class, invariance, under turbulization100 Godbillon — Vey class, naturality of81 Godbillon — Vey class, nonvanishing of347—348 Godbillon — Vey class, not a homotopy invariant99 Godbillon — Vey number101 Godbillon — Vey number, continuous variation of101 Godbillon — Vey number, invariance under cobordism101 Goodman, S.147252 gr(G)312 Graph157 Graph, closed157 Group of periods219 Group, Archimedean ordered213 Group, Archimedean ordered, Hoelder's theorem213 Group, general linear288—290 Group, Lie, action of284 Group, Lie, foliation by cosets1037 Group, Lie, locally free action of285 Group, ordered212 Group, special linear11 Groupoid5962 Growth function311 Growth type311 Growth type of a covering space318319 Growth type of a function312 Growth type of a group317 Growth type of a group orbit319 Growth type of a leaf313 Growth type of a manifold312 Growth type of a pseudogroup orbit320 Growth type, exactly polynomial313 Growth type, exponential314 Growth type, fractional316 Growth type, linear313 Growth type, nonexponential315 Growth type, quadratic313 Growth type, quasi-polynomial315 Growth type, subexponential315 Growth type, weakly polynomial316 gv()3881 Haar measure287 Haefliger structure99 Haefliger, A.137151162189 Hahn — Banach theorem241 Halmos, P.306 Hausdorff metric (or distance)362 Hausdorff — Banach — Tarski paradox306 Hector, G.65165171 Herman, M.218 hessian152 Hilbert space, lamination of299 Hirsch foliation, construction371 Hirsch foliation, entropy of373 Hirsch foliation, Godbillon — Vey class of373 Hirsch, M.W.370 Holonomy45—67 Holonomy cocycle28280 Holonomy cocycle for a foliated bundle50 Holonomy germ59 Holonomy germ, an invariant of homotopy60 Holonomy group281 Holonomy group of a leaf62 Holonomy group, germinal (of a leaf)46 Holonomy group, infinitesimal (of a leaf)4666 Holonomy group, total213 Holonomy group, total (of a foliated bundle)45—55 Holonomy groupoid4662 Holonomy homomorphism(s) of a leaf63280 Holonomy homomorphism(s), conjugate64 Holonomy homomorphism(s), infinitesimal (of a leaf)66 Holonomy homomorphism(s), total (of a foliated bundle)48 Holonomy pseudogroup55—59280 Holonomy pseudogroup of a foliated manifold46 Holonomy pseudogroup of a foliated space280 Holonomy pseudogroup of a foliation59 Holonomy pseudogroup of a regular foliated atlas59280 Holonomy transformation58 Holonomy transformation, total (of a foliated bundle)51 Holonomy, fixed point of133—134 Holonomy, germinal59—67 Holonomy, trivial of a leaf65 Holonomy, trivial of an open, saturated set205—208 Holonomy, unbounded173 Homology 3-sphere148 Homology class defined by a compact leaf138245 Homology direction254 Homology intersection138 Homotopy of foliations98 Homotopy, integrable (of foliations)96 Homotopy, piecewise (of foliations)98 Hopf fibration268 Hopf, E.306 Hurder, S.194340348 Hyperbolic plane11 Hyperbolic plane, a leaf at infinite level194 Hyperbolic plane, Poincare disk model104 Hyperbolic surface294 Imanishi, H.209 Inaba, T.194 Incomplete foliated bundle49 Infinite jail cell window311 Infinite jungle gym311 Infinite Loch Ness monster111311332 Infinite repetition181198 Infinitesimally -trivial91 Infinitesimally trivial (at boundary)91 Integrability condition36 Integral manifold36 Inverse limit276281 Inverse system281
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